This phase I trial studies the side effects and the best dose of lenalidomide when given together with cetuximab in treating patients with colorectal cancer or head and neck cancer that has spread to other places in the body and usually cannot be cured or controlled with treatment. Biological therapies, such as lenalidomide, use substances made from living organisms that may stimulate the immune system in different ways and stop tumor cells from growing. Monoclonal antibodies, such as cetuximab, may block tumor growth in different ways by targeting certain cells. Giving lenalidomide together with cetuximab may be a better treatment for colorectal cancer or head and neck cancer.

PRIMARY OBJECTIVES:

I. To determine the maximum-tolerated dose of lenalidomide when given in combination with cetuximab in patients with advanced colorectal or squamous cell head and neck cancer.

SECONDARY OBJECTIVES:

I. To evaluate response in refractory V-Ki-ras2 Kirsten rat sarcoma viral oncogene homolog (KRAS) wild-type colorectal and head/neck cancers as monitored by measurable disease by Response Evaluation Criteria In Solid Tumors (RECIST) criteria.

II. To measure antibody-dependent cytotoxic activity (ADCC) in patients receiving lenalidomide plus cetuximab.

III. To measure natural killer cell cytokine production in patients receiving lenalidomide plus cetuximab.

IV. To describe fragment c gamma receptor polymorphisms. (Exploratory) V. To describe baseline immune cell function. (Exploratory)

OUTLINE: This is a dose-escalation study of lenalidomide.

Patients receive lenalidomide orally (PO) once daily (QD) on days 1-21 and cetuximab intravenously (IV) over 1-2 hours on days 1 and 15. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 6 weeks.

Inclusion Criteria:

• Patients must have histologically or cytologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective; eligible malignancies include: colorectal cancer KRAS wild-type and squamous cell head and neck cancer
• No curative intent therapy available; there is no limit on prior number of therapies; prior epidermal growth factor receptor (EGFR)-directed therapy (tyrosine kinase inhibitors and monoclonal antibodies - including cetuximab, panitumumab, or investigational EGFR directed monoclonal antibodies) will be allowed in the phase I dose escalation; patients who have received monoclonal antibody therapy must be off all monoclonal antibodies four weeks (28 days) prior to study treatment; no chemotherapy within 28 days of trial medication
• There will be an expansion cohort for colorectal cancer patients only; for the expansion cohort, there is no limit on prior chemotherapy; the colorectal expansion cohort will include patients with cetuximab or panitumumab-resistant or refractory disease (progression during cetuximab/panitumumab therapy or within 3 months of cetuximab/panitumumab therapy
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky > 60%)
• Life expectancy of greater than 3 months
• Leukocytes > 3,000/mcL
• Absolute neutrophil count > 1,500/mcL
• Platelets > 100,000/mcL
• Total bilirubin within normal institutional limits
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) < 2.5 x institutional upper limit of normal
• Creatinine clearance > 60 mL/min/1.73 m^2 as calculated using modified Cockcroft-Gault formula
• Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days and again within 24 hours prior to starting cycle 1 of lenalidomide; further, they must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control: one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before starting lenalidomide; FCBP must also agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with a FCBP, even if they have had a successful vasectomy; a FCBP is a sexually mature woman who: 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); all patients must be counseled by a trained counselor every 28 days about pregnancy precautions and risks of fetal exposure
• Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy
• All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure
• Able to take aspirin (81 or 325 mg) daily for prophylactic anticoagulation (patients intolerant to aspirin may use warfarin or low molecular weight heparin)

Exclusion Criteria:

• Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events (>= grade 3) due to agents administered more than 4 weeks earlier
• Patients may not be receiving any other investigational agents
• Uncontrolled brain metastases; patients who have received definitive therapy, including radiation, and are not requiring ongoing medical therapy (i.e. steroids) for brain metastases will be allowed
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to lenalidomide or cetuximab or other agents used in study
• Patients with a recent history of deep vein thrombosis (DVT)/pulmonary embolism (PE) requiring therapy (within 3 months)
• Patients with history of toxicity >= grade 3 with prior EGFR directed therapy
• Patient with confirmed history of interstitial lung disease
• Uncontrolled concurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with either agent
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible