• Histologically-documented urothelial carcinoma (squamous differentiation or mixed cell types allowed if urothelial carcinoma is present)

• Metastatic disease or unresectable locally-advanced disease

• Must have received prior treatment with a checkpoint inhibitor (CPI). A CPI is defined as a programmed cell death protein 1 (PD-1) or programmed death-ligand 1 (PD-L1) inhibitor alone or with any other combination

• Must either have prior treatment with platinum-containing chemotherapy or be ineligible at time of enrollment

• Recovery to baseline or =\< grade 1 Common Terminology Criteria for Adverse Events (CTCAE) v5.0 from toxicities related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy

• Tumor tissue samples must be available for submission prior to initiation of study treatment or patient must be willing to undergo repeat tumor biopsy

• Must have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) (Version 1.1)

• An Eastern Cooperative Oncology Group (ECOG) performance status score of =\< 2

• Must be \>= 18 years of age

• Absolute neutrophil count (ANC) \>= 1500/uL without granulocyte colony-stimulating factor support (within 28 days before first dose of study treatment)

• White blood cell count \>= 2500/uL (within 28 days before first dose of study treatment)

• Platelets \>= 100,000/uL without transfusion (within 28 days before first dose of study treatment)

• Hemoglobin \>= 9 g/dL (within 28 days before first dose of study treatment)

• Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) =\< 3 x upper limit of normal (ULN). ALP =\< 5 x ULN with documented bone metastases (within 28 days before first dose of study treatment)

• Total bilirubin =\< 1.5 x ULN (for subjects with Gilbert's disease =\< 3 x ULN) (within 28 days before first dose of study treatment)

• Prothrombin (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test \< 1.3 x the laboratory ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants (within 28 days before first dose of study treatment)

• Calculated creatinine clearance \>= 30 mL/min (\>= 0.5 mL/sec) using the Cockcroft-Gault equation (within 28 days before first dose of study treatment)

• Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol), or 24-hour (h) urine protein =\< 1 g (within 28 days before first dose of study treatment)

• Capable of understanding and complying with the protocol requirements and must have signed the informed consent document

• Sexually active fertile subjects and their partners must agree to use medically accepted methods of contraception (e.g., barrier methods, including male condom, female condom, or diaphragm with spermicidal gel) during the course of the study and for 4 months after the last dose of study treatment

• Female subjects of childbearing potential must not be pregnant at screening. Female subjects are considered to be of childbearing potential unless one of the following criteria are met: documented permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes. In addition, females \< 55 years-of-age must have a serum follicle stimulating (FSH) level \> 40 mIU/mL to confirm menopause). Note: Documentation may include review of medical records, medical examinations, or medical history interview by study site