WASHINGTON—Seeking to attract millions more passengers, Amtrak is preparing an overhaul of its national network targeting increased service in the South and West—at the expense of long-haul routes beloved by train buffs and their allies in Congress.

The goal is to revamp the way Amtrak runs trains on the aging network of national routes it already maintains, with more frequent service between pairs of cities, such as Atlanta and Charlotte, N.C., or Cleveland and Cincinnati. Running more trains over shorter distances would...