Inclusion Criteria:

          -  DOSE ESCALATION PHASE

          -  Patients must have histologically confirmed malignancy that is metastatic or
             unresectable and for which standard curative or palliative measures do not exist or
             are no longer effective

          -  DOSE EXPANSION PHASE

          -  Patients must have histologically confirmed uterine serous carcinoma with at least one
             lesion suitable for biopsy without significant risk to the patient

          -  Patient disease must be evaluable or measurable by Response Evaluation Criteria in
             Solid Tumors (RECIST) version 1.1

          -  DOSE ESCALATION AND DOSE EXPANSION PHASES

          -  Patients must have had at least one prior line of cytotoxic chemotherapy

          -  Patients can have received an unlimited number of additional lines of chemotherapy,
             targeted therapy, biologic therapy, or hormonal therapy

          -  Patients must have HER2-positive or HER2-expressing tumors determined by a Clinical
             Laboratory Improvement Act (CLIA)-certified laboratory. Specific requirement of HER2
             status is outlined below:

               -  HER2 1-3+ expression by IHC OR

               -  HER2 amplification by next generation sequencing panel (NGS) or in situ
                  hybridization (ISH) OR

               -  If local testing is not feasible, patients will submit archival tissue for
                  central HER2 testing to determine eligibility. Patients with unknown or negative
                  HER2 testing will not be eligible

          -  Patients must have archival formalin-fixed paraffin-embedded (FFPE) tissue available
             for central confirmation of HER2 testing

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 70%)

          -  Hemoglobin >= 10.0 g/dL (within 14 days of randomization/enrollment)

          -  Absolute neutrophil count >= 1,000/mcL (within 14 days of randomization/enrollment)

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

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

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

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN), (< 3 x ULN in the
             presence of documented Gilbert's syndrome or liver metastases at baseline) (within 14
             days of randomization/enrollment)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x institutional ULN (within 14 days of randomization/enrollment)

          -  International normalized ratio (INR) =< 1.5 x ULN/prothrombin time (PT) and activated
             partial thromboplastin time (aPTT) (within 14 days of randomization/enrollment)

          -  Creatinine =< 1.5 x institutional ULN (within 14 days of randomization/enrollment) OR

          -  Glomerular filtration rate (GFR) >= 51 mL/min/1.73 m^2 unless data exists supporting
             safe use at lower kidney function values, no lower than 30 mL/min/1.73 m^2 (using the
             Cockcroft-Gault Equation) (within 14 days of randomization/enrollment)

          -  Patients must have left ventricular ejection fraction (LVEF) >= 50% by either an
             echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 28 days before
             randomization/enrollment

          -  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 an undetectable viral load and a CD4 count >= 250 cells/uL 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

          -  Patients with brain metastases should be stable and off steroids and at least 4 weeks
             from radiation at the time of registration

          -  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

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be better than class 2B

          -  The effects of DS-8201a and olaparib on the developing human fetus are unknown. For
             this reason and because HER2 antibody conjugated to a topoisomerase 1 inhibitor agents
             as well as PARP inhibitors are known to be teratogenic; thus, women of child-bearing
             potential and men must agree to use highly effective 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 4 months after completion of DS-8201a and
             olaparib 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 4 months after the final study drug administration.
             Preservation of sperm should be considered prior to enrollment 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 who have had chemotherapy (including antibody drug therapy) within 4 weeks
             with the following exceptions: 1 week for weekly paclitaxel; 2 weeks or five
             half-lives, whichever is longer, for small-molecule targeted agents such as
             5-fluorouracil-based agents, folinate agents, hormonal agents; or 6 weeks for
             nitrosoureas or mitomycin C

          -  Patients who have had radiation therapy within 4 weeks

          -  Patients who have had a major surgery within 4 weeks

          -  Patients who are receiving any other investigational agents

          -  For the dose expansion cohort: Patients who have received prior PARP inhibitors

          -  Patients with a history of (non-infectious) interstitial lung disease
             (ILD)/pneumonitis that required steroids, has current ILD/pneumonitis, or where
             suspected ILD/pneumonitis cannot be ruled out by imaging at screening

          -  Patients with clinically severe 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

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to DS-8201a, the inactive ingredients in the drug product, olaparib, or
             severe hypersensitivity to other monoclonal antibodies

          -  Patients receiving any medications or substances that are moderate or strong
             inhibitors or inducers of CYP3A are ineligible. Because the lists of these agents are
             constantly changing, it is important to regularly consult a frequently-updated medical
             reference. As part of the enrollment/informed consent procedures, the patient will be
             counseled on the risk of interactions with other agents, and what to do if new
             medications need to be prescribed or if the patient is considering a new
             over-the-counter medicine or herbal product

          -  Patients with a medical history of myocardial infarction within 6 months before
             randomization/enrollment, symptomatic congestive heart failure (CHF) (New York Heart
             Association class IIb to IV), troponin levels consistent with myocardial infarction as
             defined according to the manufacturer 28 days prior to randomization

          -  Patients with a corrected QT interval (QTc) prolongation to > 470 ms (females) or >
             450 ms (males) based on average of the screening triplicate 12-lead electrocardiogram
             (ECG)

          -  Patients with clinically significant corneal disease in the opinion of the
             investigator

          -  Patients with multiple primary malignancies within 3 years, except adequately resected
             non-melanoma skin cancer, curatively treated in-situ disease, and other solid tumors
             curatively treated

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

          -  Patients receiving chloroquine or hydroxychloroquine will require a washout period of
             >= 14 days to be eligible for the study

          -  Patients with unresolved toxicities from previous anticancer therapy, defined as
             toxicities (other than alopecia) not yet resolved to grade =< 1 or baseline. Subjects
             with chronic grade 2 toxicities may be eligible per the discretion of the investigator
             after consultation with the sponsor medical monitor or designee (e.g., grade 2
             chemotherapy-induced neuropathy)

          -  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 other agents used in this study