Enhancing Opportunities for Medical Doctors Act of 2017 This bill amends title XVIII (Medicare) of the Social Security Act to redistribute unused residency positions for which graduate medical education costs are paid under Medicare. Specifically, the Centers for Medicare & Medicaid Services must: (1) reduce a hospital's resident limit by a specified amount if the hospital has unused residency positions and is not a rural hospital with fewer than 250 acute care inpatient beds, and (2) increase the resident limit for each qualifying hospital that applies for an increase. In aggregate, the number of increased positions shall equal the number of reduced positions. The bill establishes specified priorities, limitations, and capacity considerations with respect to redistribution.