This study involves another course of radiation (called re-irradiation) to the participant's tumor. The type of radiation is called stereotactic body radiation therapy (SBRT). The purpose of this study is to compare the effects, good and/or bad, of different doses of SBRT given along with the chemotherapy drug, cisplatin. The researchers want to see which dose of radiation will work best in controlling the growth of head/neck cancer. The usual treatment for head/neck cancer that has grown is surgery and/or more radiation with various chemotherapy drugs.

Stereotactic Body Radiation Therapy (SBRT) is a relatively new radiation technique in which a few very high doses of radiation are delivered to small, well-defined tumors. It has been used effectively in other cancers like lung and liver. The goal is to deliver a radiation dose that is high enough to kill the cancer while limiting radiation to surrounding healthy organs. The daily dose of radiation is 2-3 times greater than conventional radiotherapy, but it is given for only 5 days over a 2 week period. Conventional radiotherapy is given over 6-7 weeks. The chemotherapy drug, cisplatin is used as a radiation sensitizer and will be given before each of the 5 radiation treatments.

Inclusion Criteria:

• Recurrence of previously pathologically proven squamous cell carcinoma of the head and neck, including original primary sites in the paranasal sinuses, nasal cavity, nasopharynx, oropharynx, oral cavity, larynx, hypopharynx, salivary glands, and/or involvement of cervical lymph nodes
• Prior radiotherapy to doses ≥ 45 Gy to the area of recurrence, ≥ 6 months prior to enrollment
• Eastern Cooperative Oncology Group (ECOG) Performance Status 0 - 2
• Life expectancy > 6 months
• Medically unfit for surgery or deemed surgically unresectable by head and neck (H&N) surgeon within 60 days prior to enrollment, or patient refusal of surgery
• Normal organ and marrow function
• No prior evidence of Grade 3 or greater toxicity or neuropathy
• Medically fit to receive cisplatin

Exclusion Criteria:

• Positive urine pregnancy test and/or breastfeeding. Women of childbearing potential or sexually active males must be willing to use effective contraception throughout their participation in the treatment phase of the study.
• Evidence of distant metastases
• Tumor size > 7 cm in one direction
• Tumor within 1 cm of the spinal cord
• Cardiac history: class III or greater congestive heart failure (CHF) or myocardial infarction (MI) within last 6 months
• Medical condition or social situation that at the discretion of the principal investigator (PI) would preclude them from completion of the trial