You can participate in this study if you:

• Age >= 18
• Zubrod (Eastern Cooperative Oncology Group [ECOG]) performance status of 0-1 within 14 days prior to registration
• Absolute neutrophil count (ANC) >= 1,500 cells/mm^3 (within 30 days prior to registration)
• Platelets >= 75,000 cells/mm^3 (within 30 days prior to registration)
• Hemoglobin >= 8.0 g/dL (within 30 days prior to registration)
• Calculated creatinine clearance (CrCl) >= 50 mL/min by the Cockcroft-Gault formula (within 30 days prior to registration)
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (within 30 days prior to registration) (not applicable to patients with known Gilbert's syndrome)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 1.5 x institutional ULN (within 30 days prior to registration)
• Known human immunodeficiency virus (HIV) infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months and CD4 T Cell count > 200 cells/mm^3 are eligible for this trial. Testing is not required for entry into protocol
• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
• Negative urine or serum pregnancy test (in persons of childbearing potential) within 14 days prior to registration. Childbearing potential is defined as any person who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes
• Willing to use highly effective contraceptives for participants of childbearing potential (participants who may become pregnant or who may impregnate a partner) during therapy and for 14 months (females); for 11 months (males) following last dose of cisplatin; this inclusion is necessary because the treatment in this study may be significantly teratogenic
• The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information

You cannot participate in this study if you:

• Patients with oral cavity cancer, nasopharynx cancer, or p16-negative cancer of unknown primary (CUP)
• Recurrence of the study cancer
• Definitive clinical or radiologic evidence of distant metastatic disease
• Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable, however, any prior exposure to cisplatin is excluded
• Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields
• Severe, active co-morbidity
• Pregnancy and individuals unwilling to discontinue nursing
• History of hypersensitivity to cisplatin or platinum-containing compounds