Lenalidomide and Cetuximab in Treating Patients With Advanced Colorectal Cancer or Head and Neck Cancer

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…