This phase II trial evaluates whether a multi-antigen vaccine called STEMVAC improves disease-free survival after surgery in patients with triple-negative breast cancer (TNBC) and moderate or extensive residual cancer burden. TNBC has an aggressive clinical course and poorer disease-free survival compared to other subtypes. While patients who have no remaining tumor in the breast or lymph nodes after surgery have excellent long-term outcomes, patients with moderate or extensive residual cancer burden remain at high risk for early disease return and poorer prognosis. STEMVAC is designed to target proteins that tumor cells use when they become more aggressive and start to spread, and it is believed to work by boosting the immune system to recognize and destroy the invader tumor cells that are causing the disease. Giving STEMVAC after surgery may improve disease-free survival rates in TNBC patients with moderate or extensive residual cancer burden.