Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed metastatic urothelial
             carcinoma; urothelial cancer derived from the bladder, ureter or upper tract is
             permitted

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) with
             conventional techniques or as >= 10 mm (>= 1 cm) with spiral computed tomography (CT)
             scan, magnetic resonance imaging (MRI), or calipers by clinical exam

          -  Patients must have access to archival tumor tissue for proposed correlative studies;
             these may be derived from transurethral resection of bladder tumors (TURBT),
             cystectomy, or biopsy; if archival tissue is not available for proposed correlatives,
             patients may be enrolled at the discretion of the study principal investigator (PI)
             (SKP)

          -  No prior cytotoxic chemotherapy for metastatic disease; prior immunotherapy is
             permitted

          -  At least 12 months have elapsed since platinum-based peri-operative treatment

          -  Karnofsky >= 70% (Eastern Cooperative Oncology Group [ECOG] performance status 0-1)

          -  Life expectancy of greater than 3 months

          -  Leukocytes >= 3,000/mcL

          -  Absolute neutrophil count >= 1,500/mcL

          -  Platelets >= 100,000/mcL

          -  Total bilirubin within institutional upper limit of normal

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional upper limit of normal

          -  Creatinine clearance >= 50 mL/min by either measured (using the Cockcroft-Gault,
             Modification of Diet in Renal Disease [MDRD] or Chronic Kidney Disease Epidemiology
             [CKD-EPI] formula) or calculated clearance (i.e. glomerular filtration rate [GFR])

          -  The effects of M6620 (VX-970) on the developing human fetus are unknown; for this
             reason and because DNA-damage response (DDR) inhibitors as well as other therapeutic
             agents used in this trial may have teratogenic potential, 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; 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 M6620 (VX-970) administration

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Radiotherapy within 4 weeks of protocol therapy

          -  Patients who are receiving any other investigational agents

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to M6620 (VX970), cisplatin, or gemcitabine

          -  M6620 (VX-970) is primarily metabolized by CYP3A4; therefore, concomitant
             administration with strong inhibitors or inducers of CYP3A4 should be avoided; because
             the lists of these agents are constantly changing, it is important to regularly
             consult a frequently-updated medical reference for a list of drugs to avoid or
             minimize use of; Patient Drug Information Handout and Wallet Card should be provided
             to patients; 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

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Pregnant women are excluded from this study because M6620 (VX-970) as a DNA-damage
             response (DDR) inhibitor 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 M6620 (VX-970), breastfeeding should
             be discontinued if the mother is treated with M6620 (VX-970); these potential risks
             may also apply to other agents used in this study

          -  Patients with >= grade 2 neuropathy