• Histologically-confirmed advanced solid tumor with measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 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)

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of BAY 1895344 in combination with gemcitabine and cisplatin in patients \< 18 years of age, children are excluded from this study

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

• Availability of archival FFPE tissue

• Prior cisplatin exposure of \< 300 mg/m\^2. Patients with prior cisplatin treatment must have received last cisplatin treatment \> 6 months prior to enrollment

• Prior treatment with PARP inhibitors is permitted (such as olaparib, rucaparib, or other experimental inhibitors of PARP administered in a clinical trial)

• Prior immune checkpoint inhibitor therapy is permitted (including anti-programmed cell death protein 1 \[PD-1\], anti-PD-ligand \[L\]1 therapy, such as pembrolizumab, nivolumab, avelumab, durvalumab, atezolizumab, or anti-cytotoxic t-lymphocyte protein 4 \[CTLA4\] therapy such as ipilimumab, or other experimental immune checkpoint pathway inhibitors administered in a clinical trial)

• Leukocytes \>= 3,000/mcL

• Hemoglobin \>= 9 g/dL

• Neutrophil count \>= 1,500/mcL

• Platelets \>= 100,000/mcL

• 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) \>= 40 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 stable brain metastases that are asymptomatic and on a stable dose of steroids are also considered eligible

• 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