Testing the Addition of an Anti-cancer Drug, BAY 1895344, to the Usual Chemotherapy Treatment (Cisplatin, or Cisplatin and Gemcitabine) for Advanced Solid Tumors With Emphasis on Urothelial Cancer

Inclusion Criteria: * 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 inhibito…