MUC1 Vaccine for Triple-negative Breast Cancer

Inclusion Criteria: * AJCC stage I-III infiltrating adenocarcinoma of the breast who have completed standard adjuvant or neoadjuvant therapy (surgery, radiation, biologic therapy, chemotherapy) for TNBC (ER-, PR-, HER-2/neu-) * Patients who have completed standard therapy for triple-negative inflammatory BC are eligible * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Absolute neutrophil count \>= 1,000/mm\^3 * Hemoglobin \>= 10.0 g/dl * Platelet count \>= 100,000/mm\^3 * Total bilirubin must be within normal limits * Transaminases (aspartate aminotransferase \[AST\] and/or alanine aminotransferase \[ALT\]) may be up to 2.5 x institutional upper limit of normal (ULN) if alkaline phosphatase is =\< ULN * Alkaline phosphatase may be up to 4 x ULN if transaminases are =\< ULN * Normal creatinine and blood urea nitrogen (BUN); if abnormal, calculated creatinine clearance must be \>= 60 mg/dL * Human immunodeficiency virus (HIV)(-), antinuclear antibody (ANA)(-), hepatitis panel (-), normal thyroid function tests; these tests will be performed at the discretion of the Investigator if warranted by history or clinical presentation * Patients must be disease-free of prior invasive malignancies for \>= 5 years, with the exception of curatively-treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix * All patients must have completed surgery with sentinel and/or axillary lymph node dissection according to participating institutional guidelines * All patients must have completed adjuvant radiation therapy according to participating institutional guidelines * All patients must have completed either adjuvant or neoadjuvant chemotherapy according to participating institutional guidelines; the choice of chemotherapy is at the discretion of the treating physician * Women of childbearing potential must have a negative pregnancy test and must be willing to consent to using an accepted and effective barrier form method of contraception during participation in the study and for a reasonable period thereafter * Patients must provide written informed consent Exclusion Criteria: * Known metastatic BC * Radiotherapy, chemotherapy, biologic therapy, or other investigational therapy within the preceding 4 weeks * Previous splenectomy or radiotherapy to spleen * Coexisting or previous malignancies except carcinoma in situ of the cervix or basal cell carcinoma of the skin * Active or uncontrolled infection * Psychiatric, addictive, or any disorder that compromises the ability to give informed consent to participate in or to comply with the requirements of the study * Concurrent systemic corticosteroid treatment - must be off all steroids for at least 4 weeks prior to vaccine administration * Any condition or behavior that in the judgment of the Investigator, would compromise the patient's ability to participate in the study