Pembrolizumab and Combination Chemotherapy Before Surgery for the Treatment of Muscle-Invasive Bladder Cancer

Inclusion Criteria: * Participants must have histologically confirmed diagnosis of muscle invasive bladder cancer (cT2-T4a, N0-N1, M0 clinical stage per American Joint Commission on Cancer \[AJCC\]). Clinical node-positive (N1) patients are eligible provided the lymph nodes (LNs) are confined to the true pelvis and are within the planned surgical LN dissection template * Histology must be either pure or predominant non-urothelial histology (noted on any TURBT) * Participants must be deemed eligible for cisplatin-based chemotherapy, radical cystectomy (RC) and pelvic lymph node dissection (PLND) by urologist and medical oncologist * Patients must agree to undergo curative intent surgery * TURBT that showed muscularis propria invasion should be within 12 weeks prior to beginning study therapy. Patients must have available tumor tissue from either initial or repeat TURBT, prior to starting study therapy. Archival tumor tissue sample of a tumor lesion (TURBT specimen) should be provided and must contain muscle invasive component, at least \>= T2 tumor. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. If submitting unstained cut slides, newly cut slides should be submitted to the testing laboratory, preferably within 14 days from the date slides are cut if possible. Patient must be willing to provide tumor tissue for research. Research samples will not be used for any studies unrelated to this trial * Must have clinical non-metastatic bladder cancer (M0) determined by cross-sectional computed tomography (CT) chest, abdomen and pelvis (CAP) or magnetic resonance imaging (MRI) imaging * A male participant must agree to use a contraception during the treatment period and for at least 180 days after the last dose of study treatment and refrain from donating sperm during this period * A female participant is eligible to participate if she is not pregnant , not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 180 days after the last dose of study treatment * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. Evaluation is to be performed within 7 days prior to the date of enrollment * Absolute neutrophil count (ANC) \>= 1500/uL (collected within 10 days prior to the start of study treatment) * Platelets \>= 100 000/uL (collected within 10 days prior to the start of study treatment) * Hemoglobin \>= 9.0 g/dL or \>= 5.6 mmol/L (collected within 10 days prior to the start of study treatment) * Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks * Serum creatinine =\< 1.5 x upper limits of normal (ULN) OR calculated creatinine clearance (glomerular filtration rate \[GFR\] can be used in place of creatinine or creatinine clearance) \>= 50 ml/min (collected within 10 days prior to the start of study treatment). Measured or calculated creatinine clearance (GFR can be used in place of creatinine clearance; 24-hour urine collection can be used for more accurate estimate as needed) * Creatinine clearance (CrCl) should be calculated per institutional standard * Total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 x ULN (collected within 10 days prior to the start of study treatment) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x ULN (collected within 10 days prior to the start of study treatment) * International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy, as long as PT is within therapeutic range of intended use of anticoagulants (collected within 10 days prior to the start of study treatment) * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy, as long as aPTT is within therapeutic range of intended use of anticoagulants (collected within 10 days prior to the start of study treatment) Exclusion Criteria: * A WOCBP who has a positive urine pregnancy test within 72 hours prior to enrollment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Patients with pure small cell histology will be excluded. Mixed histology including partial neuroendocrine small cell features will be permitted * Patients considered to be medically unfit for accelerated (dose dense) MVAC chemotherapy, TURBT or RC (per investigator discretion) will be excluded * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137) * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks. Intravesical therapies are allowed without specified treatment interval * Note: Participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline. If participant had major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment * Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and should not have active radiation pneumonitis * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, a version of varicella/zoster (chicken pox), yellow fever, rabies, Bacillus calmette-guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent * Has diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing \> 10 mg daily of prednisone dose equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug * Has known additional malignancy that is progressing or has required active systemic treatment within the past 2 years. Note: Participants with basal cell carcinoma or squamous cell carcinoma of the skin, or any carcinoma in situ that have undergone potentially curative therapy are not excluded. Low/intermediate risk prostate cancer with prior potentially curative therapy, or no intent of future systemic therapy and/or radiation is allowed. Non-invasive (Tis, Ta) upper urinary tract (renal pelvis/ureter) is allowed. Urethra cancer with prior curative intent therapy with no active recurrence is also allowed regardless of time elapsed * Has known locally advanced (unresectable) or metastatic cancer on baseline radiographic imaging (CT or MRI) obtained within 28 days prior to study registration * Has severe hypersensitivity (\>= grade 3) to pembrolizumab and/or any of its excipients * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. Note: Patients with active well controlled type 1 diabetes mellitus, vitiligo, Graves' disease, Hashimoto disease, eczema, lichen simplex chronicus, or psoriasis, not requiring systemic immunosuppression within the past 2 years are not excluded * Has history of (non-infectious) pneumonitis that required steroids or has current pneumonitis * Has an active infection requiring systemic therapy * Has known history of human immunodeficiency virus (HIV). Note: no HIV testing is required * Has known history of active hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] detected) or known active hepatitis C virus (defined as hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] detected) infection. Note: no testing for hepatitis B and hepatitis C is required * Has known history of active TB (Bacillus tuberculosis). Note: no testing is required unless it is clinically indicated * Has history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Has had allogeneic solid visceral organ transplant