COHORT A: Patients receive pembrolizumab intravenously (IV) over 30 minutes on day 1. Treatment with pembrolizumab repeats every 21 days for up to 17 courses after chemoradiation if no residual disease is found or for up to 35 courses after chemoradiation if residual disease is found. After 3 days, patients undergo surgery. Within 42 days of surgery, patients also receive docetaxel IV over 1 hour once weekly (Q1W) and doxorubicin hydrochloride IV Q1W, and undergo intensity-modulated radiation therapy (IMRT) once daily 5 days per week for 6.5 weeks in the absence of disease progression or unacceptable toxicity.