Radiotherapy Dose Escalation in Locally Advanced Squamous Cell Carcinoma of the Larynx or Hypopharynx

Inclusion Criteria: * At least 18 years of age (no upper age limit) * Biopsy proven squamous cell carcinoma of the glottis or supraglottic larynx or hypopharynx with the following T,N and M stages: * Glottic Larynx: T3-4: Any primary tumor volume * Supraglottic Larynx: T2: Primary tumor volume \> 4.0cc T3-4: Any primary tumor volume * Hypopharynx: T2: Primary tumor volume \> 4.0cc T3-4: Any primary tumor volume * N-Stages (the same for all primary sites): All N-stages * M-Stages (the same for all primary sites): M0 or M1suitable for curative attempt with Stereotactic Body Radiation Therapy. * Radiologic evaluation of the chest within 12 weeks prior to treatment; at a minimum, chest x-ray is required. CT imaging of the chest or PET/CT is acceptable. * ECOG Performance Status 0-2 * CBC/differential obtained within 8 weeks prior to treatment, with adequate bone marrow function defined as follows: * Platelets ≥ 100,000 cells/mm3 * Hemoglobin ≥ 8.0 g/dl (Note: The use of transfusion or other intervention to achieve Hgb ≥ 8.0 g/dl is acceptable.) * Adequate renal and hepatic function within 4 weeks prior to treatment, defined as follows: * Serum creatinine \< 2.0 mg/dl * Total bilirubin \< 2 x the institutional ULN * AST or ALT \< 3 x the institutional ULN. \*Note that physician attestation of patient having no known history of liver disease can take the place of bilirubin and AST/ALT labs. * Negative pregnancy test within 2 weeks prior to treatment for women of childbearing potential * Women of childbearing potential and male participants who are sexually active must practice adequate contraception during treatment and for 6 weeks following treatment. * Patients must be deemed able to comply with the treatment plan and follow-up schedule. * Patients must provide study specific informed consent prior to study entry Exclusion Criteria: * Prior history of radiation therapy to the head and neck that would likely increase the risk of serious complications from the RT delivered on this protocol * Prior history of head and neck cancer with the exception of nonmelanoma skin cancer. * Currently taking Disease Modifying Rheumatoid Drugs (DMRDs) * Severe, active co-morbidity, defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; Note, however, coagulation parameters are not required for entry into this protocol. * Pre-existing ≥ grade 2 neuropathy * Prior organ transplant * Systemic lupus * Psoriatic arthritis. * Known HIV positive. HIV positive patients are known to have worse clinical outcomes especially for local, regional, and distant cancer control. This poorer prognosis is thought to be secondary to a compromised immune system.