The purpose of this study is to find out if the experimental drug pralatrexate with the vitamins folic acid and vitamin B12 might be an effective treatment for head and neck cancer. The reason we are doing this study is because another drug called methotrexate has been used for a long time to treat head and neck cancer patients. Pralatrexate was designed by scientists to be a new drug that works better than methotrexate. Laboratory studies have shown that pralatrexate works better than methotrexate at killing cancer cells.

Pralatrexate has already been studied in patients with other types of cancers, such as lymphoma and lung cancer. The results from those studies were promising. Pralatrexate was recently approved by the Food and Drug Administration (FDA) as a new treatment for a cancer called peripheral T cell lymphoma.

Inclusion Criteria:

• Patients must have histopathologically confirmed recurrent and/or metastatic squamous cell carcinoma of the head and neck, including unknown primary squamous cell carcinomas of the neck. Confirmation of biopsy/diagnosis will be performed at MSKCC or at participating sites (NYU Cancer Institute/NYU Medical Center/ Bellevue Hospital Center).
• Patients must be at least 18 years of age.
• ECOG performance status must be ≥ 0 or 1.
• Disease must be measurable by RECIST version 1.1 criteria.
• Patients must have been previously treated with systemic chemotherapy (i.e., chemotherapy and/or targeted therapies such as cetuximab for recurrent/metastatic HNSCC,.
• At least four weeks must have elapsed from previous radiation therapy. Patients must have recovered from the acute toxic effects of treatment prior to study enrollment.
• Patients must have adequate organ function, as follows:

Adequate bone marrow reserve: absolute neutrophil count (ANC) > 1,000 cells/mm3, platelets > 100,000 cells/mm3, and hemoglobin > 9 g/dL Hepatic: AST and ALT ≤ 3 X upper limit of normal (ULN); AST and ALT ≤ 5 X ULN if liver metastasis present; Total bilirubin ≤ 1.5 x ULN unless Gilbert's disease is present Renal: Serum creatinine ≤ 1.5 mg/dL or creatinine clearance (by either 24 hour urine collection or Cockcroft-Gault equation) > or = to 55 ml/min

• Both women and men and members of all races and ethnic groups are eligible for this trial.
• Women of childbearing potential must have a negative serum pregnancy test within 14 days of treatment. Both men and women must agree to use a reliable method of birth control until 30 days following the last dose of study drug.

Exclusion Criteria:

• History of any brain metastases unless resected with no evidence for > 12 weeks and not on steroids
• Women who are lactating
• Other active malignancy, other than indolent malignancies which the investigator determines are unlikely to interfere with treatment and safety analysis
• Patients who have undergone an allogeneic stem cell transplant