Cisplatin, Docetaxel, and Pembrolizumab in Treating Patients With Stage II-III Laryngeal Cancer

Inclusion Criteria: * Newly diagnosed, previously untreated, histologically confirmed stage II to III larynx squamous cell carcinoma will be enrolled in this study * A male participant must agree to use a contraception during the treatment period and for at least 150 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 150 days after the last dose of study treatment * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Have provided archival tumor tissue sample (minimum of 20 unstained slides) or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the date of allocation * Absolute neutrophil count (ANC) \>= 1500/ul (within 10 days prior to the start of study treatment) * Platelets \>= 100000/ul (within 10 days prior to the start of study treatment) * Hemoglobin \>= 9.0 g/DL or \>= 5.6 mmol/L (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) * Creatinine OR measured or calculated (creatinine clearance \[CrCl\] should be calculated per institutional standard) creatinine clearance (glomerular filtration rate \[GFR\]: can also be used in place of creatinine or CrCl): =\< 1.5 x ULN OR \>= 30 mL/min for participant with creatinine levels \> 1.5 x institutional upper limit of normal (ULN) (within 10 days prior to the start of study treatment) * Total Bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin level \> 1.5 x ULN (within 10 days prior to the start of study treatment) * ALT (SGPT) = alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT) = aspartate aminotransferase (serum glutamic oxaloacetic transaminase); =\< 2.5 x ULN (=\< 5 X ULN for participants with liver metastases (within 10 days prior to the start of study treatment) * International normalized ratio (INR) OR prothrombin time (PT) activated partial thromboplastin time (aPTT): =\< 1.5x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants (within 10 days prior to the start of study treatment) Exclusion Criteria: * Participants are excluded from the study if any of the following criteria apply: a WOCBP who has a positive urine pregnancy test within 72 hours prior to treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * 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 (eg, CTLA-4, OX 40, CD137) * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to study treatment. Note: participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline. Participants with =\< grade 2 neuropathy may be eligible. Note: if participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment * 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, 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 (eg, 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 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 to the first dose of study drug, with the exception of dexamethasone, that can be given the day prior (D0) until 4 days after chemotherapy (D4) up to 16 mg per day for prevention of chemotherapy-induced nausea, fluid retention, and/or allergic reaction * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Note: participants with basal or squamous cell carcinoma of the skin, transitional cell carcinoma of urothelial cancer, carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy, and prostate cancer patients in active surveillance are not excluded * 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 (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis * Has an active infection requiring intravenous antibiotics therapy * Has a known history of human immunodeficiency virus (HIV) * Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV ribonucleic acid \[RNA\] \< 615 IU/L) infection. Note: no testing for hepatitis B and hepatitis C is required unless mandated by local health authority * Has a known history of active TB (Bacillus tuberculosis) * Has a 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 * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 150 days after the last dose of trial treatment * Has had a solid organ transplant and/or allogenic bone marrow transplant