Bags that exceed the maximum linear size dimensions can still be brought aboard the train, but will be subject to an additional $20 fee each way. Keep in mind that overweight bags are not permitted on Amtrak and will need to be repacked in the station. Additional bags can be purchased for some routes at $20 apiece each way, but it's best to check with Amtrak ahead of time to be sure that additional checked bags are available on your route.