Inclusion Criteria:

          -  Histologically-confirmed advanced solid tumor with measurable disease by Response
             Evaluation Criteria in Solid Tumors (RECIST) version (v)2.0 criteria, for which
             cisplatin-based therapy would be considered appropriate, including:

               -  Non-small cell lung cancer (NSCLC)

               -  UC

               -  Penile cancer

               -  Malignant pleural mesothelioma

               -  Small cell lung cancer

               -  Biliary tract cancer

               -  Esophageal and gastric cancers

               -  Ovarian cancer

               -  Endometrial cancer

               -  Cervical cancer

               -  Head and neck cancer

               -  Triple-negative breast cancer (Her2/neu-negative, estrogen receptor
                  [ER]/progesterone receptor [PR]-negative breast cancer)

          -  For the expansion cohort of the triplet combination at MTD/RP2D only:

               -  Patients with histologically confirmed advanced or unresectable urothelial
                  carcinoma are eligible

               -  The histology should be predominantly urothelial (>= 50% of sample evaluated
                  contains urothelial histology)

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Availability of archival FFPE tissue

          -  Prior cisplatin exposure of < 300 mg/m^2, with last cisplatin treatment > 6 months
             prior to enrollment is permitted

          -  Prior treatment with PARP inhibitors is permitted

          -  Prior immune checkpoint inhibitor therapy is permitted

          -  Leukocytes >= 3,000/mcL

          -  Hemoglobin >= 9 g/dL

          -  Neutrophil count >= 1.5 K/mm^3

          -  Platelets >= 100 K/mm^3

          -  Total bilirubin =< 2 mg/dL

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) =<
             3 x institutional upper limit of normal (ULN)

          -  Creatinine clearance >= 40 mL/min OR glomerular filtration rate (GFR) >= 60
             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

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

          -  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 treated brain metastases are eligible if follow-up brain imaging after
             central nervous system (CNS)-directed therapy shows no evidence of progression

          -  Patients with new or progressive brain metastases (active brain metastases) or
             leptomeningeal disease are eligible if the treating physician determines that
             immediate CNS specific treatment is not required and is unlikely to be required during
             the first cycle of therapy

          -  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 class 2B or better

          -  The effects of BAY 1895344, cisplatin, and gemcitabine on the developing human fetus
             are unknown. For this reason and because deoxyribonucleic acid (DNA)-damage response
             inhibitors agents as well as other therapeutic agents used in this trial are known to
             be teratogenic, 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 and for the duration of study participation and for 6 months after completion of
             BAY 1895344 administration. 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 BAY 1895344 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:

          -  Life expectancy < 6 weeks by investigator assessment

          -  History of prior malignancy requiring intervention in the past 3 years, except for
             cutaneous malignancies that require resection, such as squamous cell carcinoma, basal
             cell carcinoma, or cutaneous melanomas

          -  Significant peripheral neuropathy or sensorineural hearing loss (< grade 1 by Common
             Terminology Criteria for Adverse Events [CTCAE])

          -  Must NOT have had prior treatment with ATR inhibitor (prior BAY1895344 or other
             investigational ATR inhibitors), or current treatment with any other investigational
             agents

          -  Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for
             nitrosoureas or mitomycin C) prior to entering the study

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to BAY 1895344 or other agents used in study

          -  Patients receiving any medications that are substrates of CYP3A4 with a narrow
             therapeutic window, or strong inhibitors/inducers of CYP3A4 are ineligible, if they
             cannot be transferred to alternative medication. 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 uncontrolled intercurrent illness

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

          -  Pregnant women are excluded from this study because BAY 1895344 as a DNA-damage
             response inhibitor, cisplatin, and gemcitabine may have 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 BAY 1895344
             breastfeeding should be discontinued if the mother is treated with BAY 1895344 and for
             4 months after end of treatment. These potential risks may also apply to other agents
             used in this study