Continued Support for Afghan Allies Act This bill requires the Department of State to take various actions to support special immigrant visa and refugee applicants from Afghanistan. Specifically, the State Department must take certain actions, such as (1) prioritize, in the evacuation of Afghanistan, bona fide special immigrant applicants and referrals to the U.S. Refugee Admissions Program; (2) provide letters of support and other related documents to ease the transit of such individuals; (3) engage with the governments of relevant countries to better facilitate the evacuation; and (4) further surge capacity to reduce application processing times for such individuals. Furthermore, the State Department must report to Congress a strategy for safely processing such applicants from Afghanistan and a plan for carrying out the actions required by this bill. The State Department must also periodically report to Congress on the progress in implementing the strategy and processing the applicants.