Chemotherapy Before Surgery and Radiation Therapy or Surgery and Radiation Therapy Alone in Treating Patients With Nasal and Paranasal Sinus Cancer That Can Be Removed by Surgery

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * General physical condition compatible with the proposed chemotherapy and surgery * Stage T3 or T4a, histologically-confirmed NPNSCC requiring orbital or skull base resection: * Stages T3 and T4a disease will be included regardless of nodal status (N0 or N1-3), provided that surgical therapy would require orbital or skull base resection * The surgical oncologist in each institution will determine the need for resection of the orbit OR base of skull at baseline for patients on both Arms A and B and following neo-adjuvant chemotherapy for patients on Arm B * Resection of skull base will be deemed necessary according to skull base bone erosion by CT or marrow involvement by MRI is noted; for any disease abutting the skull base; or for ethmoid sinus or frontal sinus involvement * Resection of orbital contents will be deemed necessary according to skull base society guidelines, based on involvement of periorbital fat documented by MRI imaging * Patients must be deemed surgically resectable by the surgical teams at each institution and must have a determination of degree of anticipated structure preservation of orbit and skull base; this needs to be determined prior to randomization * Patients may not be receiving investigational agents at time of registration, or at any time while on study and during the 4 weeks preceding enrollment * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to docetaxel and/or both platinum-based chemotherapy agents are excluded; patient must be able to receive at least one of the two proposed chemotherapy regimens * Patients with evidence of distant metastases or leptomeningeal disease (LMD) are excluded * Patients must not have received previous irradiation for head and neck tumor, skull base, or brain tumors * Patients with uncontrolled inter-current illnesses which in the opinion of the investigator will interfere with the ability to undergo therapy including chemotherapy are excluded * Patients with a history of a different malignancy are excluded, unless the disease has not progressed for \>= 2 years * Absolute neutrophil count (ANC) \> 1500/mm\^3 =\< 2 weeks prior to randomization * Hemoglobin (Hgb) \> 8.0 g/dL =\< 2 weeks prior to randomization * Platelet count \> 100,000/mm\^3 =\< 2 weeks prior to randomization * Creatinine clearance of \> 60 ml/min; creatinine clearance may be measured or calculated; if calculating, creatinine clearance, use the Cockroft-Gault formula =\< 2 weeks prior to randomization * Total bilirubin within normal limits (must be obtained =\< 2 weeks prior to randomization) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) must be within the range allowing for eligibility, must be obtained \< 2 weeks prior to randomization * Alkaline phosphatase must be within the range allowing for eligibility, must be obtained \< 2 weeks prior to randomization * Patients with a prior history of squamous cell or basal carcinoma of the skin or in situ cervical cancer must have been curatively treated * No current peripheral neuropathy \> grade 2 at time of randomization * Patients must not have any co-existing condition that would preclude full compliance with the study; no prior history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 * Women must not be pregnant or breast-feeding * All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy * A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study * Patients must have measurable disease; MRI and/or PET/CT scans need to be performed within 2 weeks prior to registration