Many years in a row carried a cat on vacation with them, bought all the coupe, driven three - two adults and a child. Three tickets were free (husband - military), and the "cat" was taken for the full cost... No one, no time tried to resettle anyone to us.
Only once the conductor tried to "press conscience": "People cannot leave the railway stations for a day, and you are bourgeois here with the cat!", "And what she said about the cat ticket, we demanded a cat shelf in response, and she, finding nothing to object to, departed...
(IMHO) So I think if the ticket is paid – the shelf is yours.
I need a cat now.)