I think (and emphasis is on think) that from a legal perspective (Ts&Cs) you have to be on the same ticket. Second best is to be on the same PNR which I have done many times.
I’ve had mulitple tickets and multiple PNRs and asked staff to manually add luggage to final destination with no issue.
Once, on a dometic flight from a small rural airport in Norway to Oslo I was fed to the dogs, and been forced to pay for my own accomodations in Oslo due to their cancellation. However, SAS (who I missed) did re-book me the next day free of charge despite not being their fault.
I have also been stranded by carrier A in Europe, not making it home for travel the next day. In these cases, they have dealt with carrier B and I have been re-booked free of charge.