Inclusion Criteria:

          -  DOSE-ESCALATION PHASE: Must have histologically confirmed advanced solid tumor
             including but not restricted to breast cancer, gastric or gastroesophageal cancer,
             colon cancer, endometrial cancer, salivary gland tumors, and hepatobiliary tumors

          -  DOSE-EXPANSION PHASE: Must have histologically confirmed advanced/metastatic
             gastroesophageal cancer (cohort A) or colorectal cancer (cohort B)

          -  DOSE-EXPANSION PHASE: Patients must have a biopsiable lesion and provide consent for
             on treatment biopsy

          -  Age >=18 years. Because no dosing or adverse event data are currently available on the
             use of AZD6738 in combination with DS-8201a in patients < 18 years of age, children
             are excluded from this study

          -  Patients must have HER2-positive or HER2-expressing tumors determined by a Clinical
             Laboratory Improvement Act (CLIA)-certified laboratory. As a rule, for HER2
             immunohistochemistry (IHC) scoring system trastuzumab for gastric cancer (TOGA)
             criteria used for gastric/gastroesophageal junction (GEJ) cancers will be employed
             (Note: in escalation phase, for breast cancer patients that are included, breast
             cancer criteria can be used). Specific requirement of HER2 status is outlined below:

               -  HER2 expression (1-3+) by IHC locally and confirmed centrally OR

               -  HER2 expression (1-3+) by IHC tested centrally OR

               -  HER2 amplification based on fluorescence in situ hybridization (FISH) or next
                  generation sequencing

          -  Must have received at least one line of systemic chemotherapy for either locally
             advanced or metastatic disease and should have either progressed on this therapy or
             been intolerant to this therapy

          -  For tumors where anti-HER2 therapy is standard of care, patients must have progressed
             on at least 1 line of anti-HER2 therapy if eligible. For patients where DS8201a is
             approved as standard of care, prior treatment with DS8201a is not allowed

          -  Must have unresectable, advanced/metastatic disease

          -  Must have at least 1 measurable lesion on computed tomography (CT) scan per Response
             Evaluation Criteria in Solid Tumors (RECIST) 1.1. Patient without measurable but
             evaluable disease are allowed for dose-escalation phase

          -  Must be willing and able to provide an adequate archival tumor sample available to
             confirm HER2 status by Central Laboratory (if local testing is used for enrollment),
             else must be willing and able to provide an adequate archival tumor sample for HER2
             testing centrally

          -  Must have Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1

          -  Must have life expectancy of at least 3 months

          -  Must have left ventricular ejection fraction (LVEF) >= 50% within 28 days before
             enrollment (study drug treatment) by either an echocardiogram (ECHO) or multigated
             acquisition (MUGA) scan

          -  Must have a negative pregnancy test (if female)

          -  Platelets >= 100,000/mcL (within 14 days before enrollment)

               -  No transfusions with red blood cells or platelets are allowed within 1 week prior
                  to screening assessment

          -  Hemoglobin >= 9.0 g/dL (within 14 days before enrollment)

          -  Absolute neutrophil count >= 1,500/mcL (within 14 days before enrollment)

               -  No administration of granulocyte colony-stimulating factor (G-CSF) is allowed
                  within 1 week prior to screening assessment

          -  Creatinine clearance > 45/mL/min (using the Cockcroft-Gault equation) (within 14 days
             before enrollment)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 5 x institutional upper limit of normal (ULN) (within 14 days before enrollment)

          -  Total bilirubin =< 1.5 x ULN if no liver metastases or < 3 x ULN with Gilbert's
             Syndrome or liver metastases at baseline (within 14 days before enrollment)

          -  Leukocytes >= 3,000/mcL (within 14 days before enrollment)

          -  Albumin > 2.5 g/dL (GEJ patients only) (within 14 days before enrollment)

          -  International normalized ratio (INR) and either partial thromboplastin time (PTT) or
             activated (a)PTT =< 1.5 x ULN (within 14 days before enrollment)

          -  Must have adequate treatment washout period before study treatment, defined as: Major
             surgery (>= 4 weeks), radiation therapy (>= 3 weeks; in case of palliative radiation
             >= 2 weeks), systemic therapy (>= 3 weeks; in case of investigational drug use >= 2
             weeks or 5 half-lives, whichever is longer)

          -  Patients who are human immunodeficiency virus (HIV) positive may participate IF they
             meet the following eligibility requirements:

               -  They must be stable on their anti-retroviral regimen, and they must be healthy
                  from an HIV perspective

               -  They must have a CD4 count of greater than 250 cells/mcL over the past 6 months
                  on this same anti-retroviral regimen and must not have had a CD4 count < 200
                  cells/mcl over the past 2 years, unless it was deemed related to THE CANCER
                  AND/OR CHEMOTHERAPY-induced bone marrow suppression

                    -  For patients who have received chemotherapy in the past 6 months, a CD4
                       count < 250 cells/mcl during chemotherapy is permitted as long as viral
                       loads were undetectable during this same chemotherapy

               -  They must have an undetectable viral load and a CD4 count >= 250 cells/mcL within
                  7 days of enrollment

               -  They must not be currently receiving prophylactic therapy for an opportunistic
                  infection and must not have had an opportunistic infection within the past 6
                  months. HIV-infected patients should be monitored every 12 weeks for viral load
                  and CD4 counts

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable on suppressive therapy, if indicated

          -  Patients with a history of hepatitis C virus (HCV) infection must have been treated
             and cured. For patients with HCV infection who are currently on treatment, they are
             eligible if they have an undetectable HCV viral load

          -  Subjects with clinically inactive brain metastases may be included. Subjects with
             treated brain metastases that are no longer symptomatic and who require no treatment
             with corticosteroids or anticonvulsants may be included in the study if they have
             recovered from the acute toxic effect of radiotherapy. A minimum of 2 weeks must have
             elapsed between the end of whole-brain radiation therapy and study treatment

          -  Patients with new or progressive brain metastases (active brain metastases) or
             leptomeningeal disease are eligible if the treating physician determines that
             immediate central nervous system (CNS) specific treatment is not required and is
             unlikely to be required for at least 4 weeks (or scheduled assessment after the first
             cycle of treatment), and a risk-benefit analysis (discussion) by the patient and the
             investigator favors participation in the clinical trial

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

          -  HER2 antibody conjugated to a topoisomerase 1 inhibitor agents as well as AZD6738 are
             known to be teratogenic; thus, women of child-bearing potential and men must agree to
             use adequate contraception (hormonal or barrier method of birth control; abstinence)
             prior to study entry, for the duration of study participation, and for at least 7
             months (women of childbearing potential [WOCBP] only) after the last dose of study
             drug. Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, she should inform her treating physician
             immediately. Men treated or enrolled on this protocol must also agree to use adequate
             contraception prior to the study, for the duration of study participation, and 6
             months after completion of study drug administration

          -  Women of non-child-bearing potential defined as pre-menopausal females with a
             documented tubal ligation or hysterectomy; or postmenopausal defined as 12 months of
             spontaneous amenorrhea (in questionable cases, a blood sample with simultaneous
             follicle-stimulating hormone [FSH] > 40 mIU/mL and estradiol < 40 pg/mL [< 147 pmol/L]
             is confirmatory) are eligible. Females on hormone replacement therapy (HRT) and whose
             menopausal status is in doubt will be required to use one of the contraception methods
             outlined for women of child-bearing potential if they wish to continue their HRT
             during the study. Otherwise, they must discontinue HRT to allow confirmation of
             post-menopausal status prior to study enrollment. For most forms of HRT, at least 2-4
             weeks will elapse between the cessation of therapy and the blood draw; this interval
             depends on the type and dosage of HRT. Following confirmation of their post-menopausal
             status, they can resume use of HRT during the study without use of a contraceptive
             method

          -  Male subjects must not freeze or donate sperm starting at screening and throughout the
             study period, and at least 6 months after the final study drug administration.
             Preservation of sperm should be considered prior to enrolment in this study

          -  Female subjects must not donate, or retrieve for their own use, ova from the time of
             screening and throughout the study treatment period, and for at least 7 months after
             the final study drug administration

          -  Ability to understand and the willingness to sign a written informed consent document.
             Participants with impaired decision-making capacity (IDMC) who have a
             legally-authorized representative (LAR) and/or family member available will also be
             eligible

        Exclusion Criteria:

          -  Patients with a history of (non-infectious) interstitial lung disease
             (ILD)/pneumonitis that required steroids, have current ILD/pneumonitis, or where
             suspected ILD/pneumonitis cannot be ruled out by imaging at screening. Patient using
             e-cigarettes/vaping are also excluded

          -  Patients with a medical history of myocardial infarction within 6 months before
             enrollment (study treatment), symptomatic congestive heart failure (New York Heart
             Association Class II to IV, corrected QT interval (QTcF) prolongation to > 470 ms
             (females) or > 450 ms (males) as corrected by Framingham's formula

          -  Patients with spinal cord compression or clinically active central nervous system
             metastases, defined as untreated and symptomatic, or requiring therapy with
             corticosteroids or anticonvulsants to control associated symptoms

          -  Patients with multiple primary malignancies within 2 years, except adequately resected
             non-melanoma skin cancer, curatively treated in situ disease, or other curatively
             treated solid tumors

          -  Patients with a history of severe hypersensitivity reactions to either the drug
             substances or inactive ingredients in the drug product

          -  Patients with an uncontrolled infection requiring IV antibiotics, antivirals, or
             antifungals

          -  Patients with substance abuse or any other medical conditions that would increase the
             safety risk to the subject or interfere with participation of the subject or
             evaluation of the clinical study in the opinion of the investigator

          -  Patients with a concomitant medical condition that would increase the risk of toxicity
             in the opinion of the investigator

          -  Patients who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities grade >1) with the exception of alopecia. Subjects
             with chronic grade 2 toxicities may be eligible per discretion of the investigator
             after discussion with study principal investigator (PI) (e.g., grade 2 chemo-induced
             neuropathy).

          -  Any previous treatment with an ATR inhibitor

          -  Patients with any clinically apparent pulmonary compromise resulting from intercurrent
             pulmonary illnesses including, but not limited to, any underlying pulmonary disorder
             (i.e., pulmonary emboli within three months of the study enrollment, severe asthma,
             severe chronic obstructive pulmonary disease [COPD], restrictive lung disease, pleural
             effusion, etc.), and any autoimmune, connective tissue or inflammatory disorders with
             potential pulmonary involvement (i.e., Rheumatoid arthritis, Sjogren's, sarcoidosis,
             etc.), or prior pneumonectomy

          -  Patients with myelodysplastic syndrome/acute myeloid leukemia or with features
             suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML)

          -  Patients unable to swallow orally administered medication and patients with
             gastrointestinal disorders likely to interfere with absorption of the study medication

          -  Concomitant use of known strong CYP3A inhibitors (e.g., itraconazole, telithromycin,
             clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir,
             saquinavir, nelfinavir, boceprevir, telaprevir). The required washout period prior to
             starting study treatment is 2 weeks. Concomitant use of known strong (e.g.,
             phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine,
             carbamazepine, nevirapine and St John's Wort ). The required washout period prior to
             starting study treatment is 5 weeks for enzalutamide or phenobarbital and 3 weeks for
             other agents

          -  Patients with a pleural effusion, ascites, or pericardial effusion that requires
             drainage, peritoneal shunt, or cell-free and concentrated ascites reinfusion therapy
             (CART). (Drainage and CART are not allowed within 2 weeks prior to screening
             assessment)

          -  Patients with previous allogeneic bone marrow transplant or double umbilical cord
             blood transplantation (dUCBT)

          -  Whole blood transfusions in the last 120 days prior to entry to the study (packed red
             blood cells and platelet transfusions are acceptable within the last 28 days as long
             as they are not within 1 week prior to screening assessment)

          -  Patients at risk of brain perfusion problems, e.g., medical history of carotid
             stenosis or pre-syncopal or syncopal episodes, history of transient ischemic attacks
             (TIAs)

          -  Uncontrolled hypertension (grade 2 or above) requiring clinical intervention

          -  Patients with relative hypotension (< 90/60 mm Hg) or clinically relevant orthostatic
             hypotension, including a fall in blood pressure of > 20 mm Hg

          -  Patients who have received corticosteroids (at a dose > 10 mg prednisone/day or
             equivalent) for any reason within 2 weeks prior to first dose

          -  Patients with uncontrolled intercurrent illness

          -  Patients with psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Pregnant women are excluded from this study because DS-8201a is a HER2 antibody
             conjugated to a topoisomerase 1 inhibitor agent with the potential for teratogenic or
             abortifacient effects. Because there is an unknown but potential risk for adverse
             events in nursing infants secondary to treatment of the mother with DS-8201a,
             breastfeeding should be discontinued if the mother is treated with DS-8201a. These
             potential risks may also apply to AZD6738

          -  Patients cannot be receiving chloroquine or hydroxychloroquine. Patients receiving
             these drugs must have a washout period of > 14 days before enrollment/randomization