If I own a private car and it has a current Amtrak inspection, they will haul it on their existing trains for $2.10 a mile (last time I looked) plus some charges for switching services, parking and the like. Additional cars on the same movement are $1.90 up to the point at which additional engines are needed. That is something around $2,000 for one car one way on their medium distance routes – say New Orleans to Chicago. The additional cost to Amtrak for doing that is some diesel fuel.
To Amtrak that is pretty close to found money, and it has the effect of reducing the subsidy needed from the public at large. Those of you who are concerned that I might somehow make a profit on the move are missing the point – it is a win-win situation.