Inclusion Criteria:  Participant has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Participant must have histologically or cytologically documented urothelial/transitional cell carcinoma of the bladder, renal pelvis, ureter or urethra. Other histologies including adenocarcinoma, squamous differentiation or mixed are eligible. Participant has locally advanced or metastatic disease that is not amenable to curative intent treatment. Participants must have measurable disease at baseline according to RECIST Version 1.1. Lesions in a prior radiation field must have progressed subsequent to radiotherapy to be considered measurable. Participant must have received prior treatment with PD-1/PD-L1 inhibitor therapy in the locally advanced or metastatic urothelial cancer setting. Participants who received PD-1/PD-L1 therapy in the neoadjuvant/adjuvant setting and had recurrent or progressive disease either during therapy or within 3 months of therapy completion are eligible.  Participant who received prior treatment with platinum-containing chemotherapy defined as those who received platinum in the neoadjuvant/adjuvant setting and had recurrent or progressive disease within 12 months of completion or received treatment with platinum in the locally advanced (defined as unresectable with curative intent) or metastatic setting.  Platinum based chemotherapy may include combination use with a PD-1 or PD-L1 inhibitor.  Participant has the following baseline laboratory data. If a participant has received a recent blood transfusion or growth factor, the hematology tests must be obtained ≥7 days after any growth factor and ≥ 28 days after any blood transfusion.  absolute neutrophil count (ANC) ≥ 1.0 × 10^9/L platelet count ≥ 100 × 10^9/L hemoglobin ≥ 9 g/dL serum total bilirubin (TBL) ≤ 1.5 × upper limit of normal (ULN) or ≤ 3 × ULN for participants with Gilbert's disease creatinine clearance (CrCl) ≥ 30 mL/min as estimated per institutional standards or as measured by 24-hour urine collection (glomerular filtration rate [GFR] can also be used instead of CrCl). alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 × ULN  Female participant is not pregnant and at least one of the following conditions apply:  Not a woman of childbearing potential (WOCBP) WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 6 months after the last dose of study treatment administration. Female participant must agree not to breastfeed starting at screening and throughout the study period and for at least 6 months after the last dose of study treatment administration. Female participant must not donate ova starting at first dose of study treatment and throughout the study period and for 6 months after the last dose of study treatment administration. Male participant with female partner(s) of childbearing potential (including breastfeeding partner) must agree to use contraception throughout the treatment period and for 6 months after the last dose of study treatment administration. Male participant must not donate sperm during the treatment period and for 6 months after the last dose of study treatment administration. Male participant with pregnant partner(s) must agree to remain abstinent or use a condom for the duration of the pregnancy throughout the study period and for 6 months after the last dose of study treatment administration. Participant agrees not to participate in another interventional study while receiving study treatment in the present study. Participant must have had progression or recurrence of urothelial cancer during or following receipt of most recent therapy. Participant must have an anticipated life expectancy of ≥ 3 months.  Exclusion Criteria:  Participant has preexisting sensory or motor neuropathy Grade ≥ 2.  Participant has active central nervous system (CNS) metastases. Participants with treated CNS metastases are permitted on study if all the following are true:  CNS metastases have been clinically stable for ≥ 6 weeks prior to screening. If requiring steroid treatment for CNS metastases, the participant is on a stable dose ≤ 20 mg/day of prednisone or equivalent for ≥ 2 weeks. Baseline imaging scans show no evidence of new or enlarged brain metastasis. Participant does not have leptomeningeal disease. Participant has ongoing clinically significant toxicity (Grade 2 or higher with the exception of alopecia) associated with prior treatment (including systemic therapy, radiotherapy or surgery). Participant with ongoing ≥ Grade 3 immunotherapy-related hypothyroidism or panhypopituitarism is excluded. Participant with ongoing immunotherapy-related colitis, uveitis, myocarditis or pneumonitis, or participants with other immunotherapy-related AEs requiring high doses of steroids (> 20 mg/day of prednisone or equivalent), is excluded. Participant with ≤ Grade 2 immunotherapy-related hypothyroidism or panhypopituitarism may be enrolled when well-maintained/controlled on a stable dose of hormone replacement therapy (if indicated). Participant has a history of uncontrolled diabetes mellitus within 3 months before the first dose of study treatment. Uncontrolled diabetes is defined as hemoglobin A1c (HbA1c) ≥ 8 percent or HbA1c between 7 percent and < 8 percent with associated diabetes symptoms (polyuria or polydipsia) that are not otherwise explained. Participant has prior treatment with enfortumab vedotin or other monomethyl auristatin E (MMAE)-based antibody-drug conjugate (ADCs). Participant has a second malignancy diagnosed within 3 years before first dose of study drug, or any evidence of residual disease from a previously diagnosed malignancy. Participants with non-melanoma skin cancer, localized prostate cancer treated with curative intent with no evidence of progression, low-risk or very low-risk (per standard guidelines) localized prostate cancer under active surveillance/watchful waiting without intent to treat, or carcinoma in situ of any type (if complete resection was performed) are allowed. Participant is currently receiving systemic antimicrobial treatment for viral, bacterial or fungal infection at the time of first dose of study treatment. Routine antimicrobial prophylaxis is permitted. Participants with a positive hepatitis B surface antigen and/or anti-hepatitis B core antibody. Participants with a negative polymerase chain reaction (PCR) assay are permitted with appropriate antiviral prophylaxis. Active hepatitis C infection or known human immunodeficiency virus (HIV) infection. Participant who have been treated for hepatitis C infection are permitted if they have documented sustained virologic response of ≥ 12 weeks. Participant has documented history of a cerebral vascular event (stroke or transient ischemic attack), unstable angina, myocardial infarction or cardiac symptoms (including congestive heart failure) consistent with New York Heart Association Class III-IV within 6 months prior to the first dose of study drug. Participant had major surgery within 2 weeks or radiotherapy, chemotherapy, biologics, investigational agents, and/or antitumor treatment with immunotherapy that is not completed 2 weeks prior to first dose of study drug. Toxicities from these therapies must have resolved or adequately stabilized before starting study treatment. Participant has known hypersensitivity to enfortumab vedotin or to any excipient contained in the drug formulation of enfortumab vedotin (including histidine, trehalose dihydrate and polysorbate 20) or participant has known hypersensitivity to biopharmaceuticals produced in CHO cells. Participant has known active keratitis or corneal ulcerations. Participant with superficial punctate keratitis is allowed if the disorder is being adequately treated. Participant has any condition which makes the participant unsuitable for study participation. Uncontrolled tumor-related bone pain or impending spinal cord compression. Participant requiring pain medication must be on a stable regimen for at least 2 weeks at the time of first dose.