HER2 Directed Dendritic Cell Vaccine, Trastuzumab, Pertuzumab, and Chemotherapy in Treating Participants with Stage II-III HER-2 Positive Breast Cancer

Inclusion Criteria

• Patients must have histologically confirmed clinical stage II or III estrogen receptor negative (ER-) progesterone receptor (PR) - HER2 positive (+) (per College of Pathologists [CAP] criteria) invasive carcinoma of the breast
• Medically and surgically appropriate to undergo neoadjuvant chemotherapy with TCH-P Taxotere (docetaxel), carboplatin, Herceptin (trastuzumab), Perjeta (pertuzumab) regimen followed by standard of care local therapy as determined by their treating physician
• Eastern Cooperative Oncology Group (ECOG) performance status < 2
• Leukocytes >= 3,000/uL
• Absolute neutrophil count >= 1,500/uL
• Platelets >= 100,000/uL
• 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 within normal institutional limits OR creatinine clearance >= 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal
• Cardiac ejection fraction within institutional normal limits by either multigated acquisition scan (MUGA) or echocardiogram (ECHO) at baseline
• Women of child-bearing potential and their male partners must agree to use adequate contraception (hormonal or 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; sexually active male participants should use a barrier method or exercise abstinence during chemotherapy administration until surgery
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria

• Patients with inflammatory breast cancer, widespread locally advanced unresectable disease involving the chest wall/nodal basins in which a curative surgical resection cannot be performed, or those in whom de novo metastatic disease is suspected or confirmed
• Patients may not be receiving any other investigational agents for the treatment of their breast cancer
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study vaccine components and any of the chemotherapy drugs (docetaxel, carboplatin, trastuzumab, pertuzumab)
• Patients who are unwilling or unable to undergo an apheresis for production of their vaccine
• Uncontrolled intercurrent 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 and women who are breastfeeding are excluded from this study
• Patients with known congenital or acquired immune deficiency (including those patients who require systemic immunosuppressant drugs for autoimmune disease or organ transplant)
• Patients with pre-existing peripheral neuropathy that would limit treatment with taxanes and platinum agents