More for Veterans Act This bill directs the Department of Defense (DOD) to ensure that retired and honorably discharged members of the Armed Forces, including members medically discharged, separated, or on the temporary disability retirement list, and their immediate family remain eligible for Military OneSource Program services for at least one year after the end of the member's tour of service, retirement date, or separation date. (Military OneSource is a DOD-funded program that provides comprehensive information on aspects of military life at no cost to active duty National Guard and Reserve Component members and their families.)