The purpose of this study is to find out if the combination of two established anti-cancer therapies are beneficial in patients with squamous cell carcinoma of the skin. Specifically, investigators want to determine if the combination of 5-FU/Capecitabine (oral pills) and Interferon alpha-2b (injection) can help people with advanced cases of squamous cell carcinoma of the skin. For participants that are not approved for oral capecitabine, treating physicians will use continuous infusion 5-FU. Both 5-FU/Capecitabine and Interferon alpha-2b have been used separately to treat squamous cell carcinoma of the skin and are FDA approved in other cancer types.

Inclusion Criteria:

• Must have histologically or cytologically confirmed squamous cell carcinoma of the skin. Potential participants who present with "squamous cell carcinoma of unknown primary lesions" at the time of diagnosis will be eligible if patients have a plausible primary skin site removed in the past. Similarly, potential participants with neck, parotid, or facial lymph nodes positive for squamous cell carcinoma with no identifiable mucosal primary would also be eligible.
• Must have measurable disease, defined by Response according to Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 as at least one lesion that can be accurately measured in at least one dimension of >10 mm by CT, MRI, or calipers
• There is no limitation to prior treatments with local, regional, topical or systemic agents, except for prior systemic treatment with 5-fluorouracil or prodrugs thereof. Prior topical treatment with 5-fluorouracil is permitted. Patients who are on chronic daily doses of prednisone of greater than 10 mg are excluded. There is no restriction on timing of last treatments as long as patients have recovered from all expected toxicities and at least 21 days have passed since last administration.
• Life expectancy of greater than 3 months
• Eastern Cooperative Oncology Group (ECOG) performance status <=2 (Karnofsky >=60%
• Must have normal organ and marrow function
• Must not be candidates for curative locoregional treatments. Patients with recurrent locoregional disease following surgery and/or radiation for who a resection is unacceptably morbid and unlikely to be curative are eligible.
• Women of child-bearing potential and men must agree to use adequate contraception (barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately.
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Have had chemotherapy or radiotherapy within 21 days (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier
• May not be receiving any other investigational agents
• Known brain metastases
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to either 5-FU/Capecitabine or Interferon
• Uncontrolled, ongoing illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, psychiatric illness/social situations that would limit compliance with study requirements
• Women who are pregnant or breastfeeding
• Any heart or lung transplant patient on immunosuppressive agents. Renal transplant patients are allowed if patient is willing to reduce immunosuppressive agents and understand risk of rejection and possible need to return to dialysis. Patients with Chronic Lymphocytic Leukemia (CLL) or other hematologic malignancies are allowed as long as they meet other criteria listed above.