Cetuximab and Pembrolizumab in Treating Patients With Colorectal Cancer That is Metastatic or Cannot Be Removed by Surgery

Participants who have had chemotherapy, targeted therapies, radiotherapy, or used an investigational device within 2 weeks prior to the first dose of treatment or those who have not recovered from adverse events (i.e., =\< grade 1 or at baseline) due to agents administered more than 2 weeks earlier; note: participants with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study

Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment

Has a known history of active TB (Bacillus Tuberculosis)

Hypersensitivity to pembrolizumab or any of its excipients

Prior severe infusion reaction to cetuximab

Has a known additional malignancy that requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer

Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; participants with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability

Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment

Has known history of, or any evidence of active, non-infectious pneumonitis

Uncontrolled clinically significant intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, unstable cardiac arrhythmia, or psychiatric illness, substance abuse disorders or social situations that would limit compliance with study requirements

Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment

Has a known history of human immunodeficiency virus (HIV or HIV 1/2 antibodies); testing not required

Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected); testing not required

Has received a live vaccine within 30 days of planned start of study therapy (note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and shingles are not allowed)

Received an investigational agent within 30 days prior to starting study treatment

Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator

Unwilling or unable to follow protocol requirements

What this study is about