CHR might not object but NR don't seem to be terribly keen to sharing stations with heritage organisations.
Where NR and heritage railways meet, the trains are normally operationally separated and usually have a separate ticket barrier, sometimes even separate buildings/entrances - Bishop Auckland, East Grinstead, Eridge, Grosmont, Keighley, Kidderminster, Paignton etc. Whitby is the only station where there's regular interaction between heritage and public service trains that I can think of, and that's a quite special case but even then still has it's own platform.