Study of 2141-V11 in People With Non-muscle Invasive Bladder Cancer That Did Not Respond to Standard Treatment

The purpose of this study is to test the safety of the study drug 2141-V11 in people whose NMIBC did not respond to standard treatment, and who will not have the standard surgical procedure to remove the bladder. The researchers will test different doses of 2141-V11 to see which dose is safest in people. The researchers will also do tests to see how the body absorbs, distributes, and gets rid of 2141-V11. This study is one of the first to test 2141-V11 in people, and the first to test 2141-V11 delivered through a catheter into the bladder.

Inclusion Criteria: Cohorts A and B Part 1 * High-grade (HG) NMIBC (HG Ta, CIS, and/or T1) of urothelial histology that is unresponsive to adequate BCG therapy. * Stage, grade, and histology must be confirmed by the MSK Department of Pathology * Subjects with tumors of mixed urothelial/non-urothelial histology may be included, but urothelial carcinoma must be the predominant histology; subjects with predominant or exclusively non-urothelial histology are excluded * In those subjects with CIS, the CIS must be present on the tumor sample from the most recent cystoscopy/TURBT * In this context, adequate BCG therapy is defined as at least one of the following: * At least five of six doses of an initial induction course plus at least two of three doses of maintenance therapy * At least five of six doses of an initial induction course plus at least two of six doses of a second induction course * Disease unresponsive to adequate BCG therapy is defined as the following. Suspected recurrence from suspicious cytology or cystoscopy, and later confirmed via TURBT, is acceptable: * Persistent or recurrent CIS alone or with recurrent Ta/T1 disease (noninvasive papillary disease/tumor invades the subepithelial connective tissue) within 12 months of completion of adequate BCG therapy * Recurrent HG Ta/T1 disease within 6 months of completion of adequate BCG therapy * HG T1 disease at the first evaluation following an induction BCG course Cohort C: * Muslce invasive bladder cancer cT2-T4aN0-2 that has a predominant urothelial histology. * Stage, grade, and histology must be confirmed by the MSK Department of Pathology * Subjects with tumors of mixed urothelial/non-urothelial histology may be included, but urothelial carcinoma must be the predominant histology; subjects with predominant or exclusively non-urothelial histology are excluded Cohort A and B Only: * In subjects with papillary tumors (Ta and T1), a complete TURBT must have been performed. This is characterized by: * Attainment of a visually complete resection of all papillary tumors (Ta and T1) * Residual CIS not amenable to complete transurethral resection is acceptable * Receipt of restaging transurethral resection for any tumor with invasion into the lamina propria (HG T1) as part of standard care, with documented presence of uninvolved detrusor muscle. * Most recent cystoscopy/TURBT must have been performed within 6 months of the first dose of trial treatment. * Absence of urothelial carcinoma involving the upper urinary tract (documented by radiological imaging or ureteroscopy). * Have elected not to undergo or are considered ineligible for radical cystectomy, as determined by the treating surgeon. Reasons for ineligibility or refusal of radical cystectomy should be discussed with the subject as part of the informed consent process. * Ineligibility factors for radical cystectomy may include, but are not limited to: * Cardiovascular disease (e.g., recent acute coronary syndrome, arrhythmia, heart failure) * Chronic obstructive pulmonary disease that would preclude a safe surgical procedure, as determined by the treating surgeon * Poor performance status * Prior major abdominal and pelvic surgery that would preclude a safe surgical procedure, as determined by the treating surgeon Cohort C Only: \- Are willing to undergo a standard of care examination under anesthesia or cystoscopy within four weeks of scheduled radical cystetomy. * Patients must have received 3-4 cycles of neoadjuvant Enfortumab Vedotin and pembrolizumab * Age ≥18 years on day of signing informed consent. * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 / Karnofsky performance status ≥60%, as assessed within 28 days prior to treatment initiation. * Required values for screening laboratory tests, performed within 28 days prior to treatment initiation: Absolute neutrophil count (ANC) ≥1000/mm3 * Platelets \>75,000/mm3 without * Hemoglobin \>8 g/dL * Creatinine clearance \>40 mL/min for the dose-escalation phases, \>25 mL/min for the dose expansion phases (estimated GFR can also be used in place of creatinine clearance) * AST/ALT ≤3 times the institutional upper limit of normal (ULN) * Total bilirubin ≤1.5 times the institutional ULN * Female subjects of childbearing potential must have a negative serum pregnancy test within 72 hours prior to receiving the first dose of study treatment. * Female subjects will be considered of non-reproductive potential if any of the following: * Postmenopausal \[defined as at least 12 months with no menses without an alternative medical cause; in women \