I’ve had limited issues with this, but it should be quite fun later in July when I am flying ARN-LHR in CE on BA, connecting to LH on LHR-MUC in preparation for LH F to the US on separate tickets and PNRs.
In my previous job, we used a TA and frequently had multiple tickets on multiple, none-aligned carriers. I once had a Passenger Name Record (PNR) containing three tickets on different ticket stock:
BGO-BHX on KLM
BHX-CDG-SIN-AMS-ARN on AF
SIN-KUL on SQ
In this case, I had no issue with interlining as everything was on one PNR. So I try to contact a TA when I have this situation so I can at least get the everything on one PNR. This tends to solve many issues as the full route is displayed to the check-in agent.