A Study to Find Out if Enfortumab Vedotin Given With Pembrolizumab Helps People With Muscle-invasive Bladder Cancer Keep Their Bladder

Inclusion Criteria:

* Participant has histologically-confirmed MIBC, stage cT2-T4aN0M0 or T1-T4aN1M0. NOTE: urothelial carcinomas (UCs) not originating from the bladder (e.g., upper tract \[ureters, renal pelvis\], urethra) are not eligible. UCs invading into the prostatic stroma with no histologic muscle invasion is allowed, provided that the extent of disease is confirmed via imaging.
* Participant has predominant UC histology (≥ 50%). NOTE: Participants with mixed histology are eligible provided the urothelial component is ≥ 50% (participants whose tumors contain predominant \[≥ 50%\] plasmacytoid variant are not eligible). Participants whose tumors contain any neuroendocrine histology are not eligible.
* Participant is deemed eligible for radical cystectomy and pelvic lymph node dissection.
* Participant has accessible archival tumor tissue from the primary tumor, for which source and availability have been confirmed prior to study intervention. If no archival tumor tissue is available, the participant will have a biopsy to obtain tumor tissue prior to study intervention.
* Participant has Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
* Have a transurethral resection of a bladder tumor within 60 days (+14 days) prior to, or during screening (from the date of informed consent form signature).

Exclusion Criteria:

* Participant has preexisting sensory or motor neuropathy Grade ≥ 2.
* Participant has ≥ N2 disease or metastatic disease (M1) as identified by imaging
* Participant has a history of uncontrolled diabetes mellitus within 3 months prior to screening. Uncontrolled diabetes (within 3 months before first dose) is defined as hemoglobin A1c (HbA1c) ≥ 8% or HbA1c between 7% and \< 8% with associated diabetes symptoms (polyuria or polydipsia) that are not otherwise explained. The lowest HbA1c during the screening period will be used to determine eligibility.
* Participant has a second malignancy diagnosed within 3 years before first dose of study intervention, or any evidence of residual disease from a previously diagnosed malignancy. Participant 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 has known active keratitis or corneal ulcerations. Participant with superficial punctate keratitis is allowed if the disorder is being adequately treated.
* Participant has a history of (non-infectious) pneumonitis/interstitial lung disease (ILD) that required steroids or has current pneumonitis/ILD.
* Participant has a history of idiopathic pulmonary fibrosis, organizing pneumonia, drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan.
* Participant has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of study intervention. Inhaled or topical steroids are permitted in the absence of active autoimmune disease. Physiologic replacement doses of corticosteroids are permitted for participants with adrenal insufficiency.
* Participant has active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs).

  * Replacement therapy (e.g., thyroxine, insulin, physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed.
  * Brief (\< 7 days) use of systemic corticosteroids is allowed when use is considered standard of care.
  * Participant with vitiligo, psoriasis, type 1 diabetes mellitus, hypothyroidism, or resolved childhood asthma/atopy will not be excluded.
  * Participant requiring intermittent use of bronchodilators, inhaled steroids, or local steroid injections will not be excluded.
  * Participant with hypothyroidism that is stable with hormone replacement therapy or Sjögren's syndrome will not be excluded.
* Participant has received prior therapy with an anti-programmed cell death protein 1 (PD-1), anti-programmed death-ligand 1 (PD-L1), or anti-programmed death-ligand 2 agent or with an agent directed to another stimulatory or coinhibitory T-cell receptor (e.g., CTLA-4, OX-40, CD137).
* Participant has received prior systemic anti-cancer therapy for MIBC/non-muscle invasive bladder cancer (NMIBC), or received prior systemic anti-cancer therapy including investigational agents (including enfortumab vedotin or other monomethyl auristatin E-based antibody-drug conjugates) within 3 years prior to screening.

NOTE: Prior treatment for NMIBC with intravesical instillation therapy such as Bacillus Calmette-Guérin or intravesical chemotherapy is permitted. Prior systemic treatment (including, but not limited to, anti-PD-1/PD-L1 treatment with pembrolizumab, etc.) received for NMIBC is not permitted.

* Participant has received a partial cystectomy of the bladder to remove any NMIBC or MIBC.
* Participant has received any prior radiotherapy to the bladder.