In Europe, a common option on sleep trains is to book night accommodation in space shared with one or more strangers. This is cheaper than a private compartment, but more expensive than having only a seat. Amtrak does not officially offer this option. If I have already booked my roomette, would it be allowed (notwithstanding practical issues) to offer roomless travellers on the same train (i.e. who already have a ticket, just no reservation) to share the roomette with me at a modest fee, or is this against Amtrak regulations?
This is a good question that should be asked to an Amtrak representative.
Technically it would not occur additional fees, since the room is already paid in full. According to stories I've heard, passengers have the option to upgrade en-route by asking the conductor; the room fare is then calculated according to the remaining distance at the current train position or passed stops.
It is technically possible to arrange some sort of shared room when on board. Getting a conductor to actually do it is a different story. What you would need to do is find your companion, and have them book an "Open Sleeper" ticket; it shouldn't have any additional costs with it. It