To get the in-detail answer to this you have to go deep into the bowels of airline technologies, so apologies in advance to all those who will be very confused by what follows.

Scenario 1: The glamorously named IATCI (inter-airline through check-in) is only designed for through itineraries on more than one airline. It’s a standardised schema that works across compatible PSSs, but won’t (and technically can’t) work if there is only one airline involved as personal data can’t be shared in these circumstances.

Scenario 2: If the two airlines happen to use the same PSS and have an interline agreement, then it may be possible to load up an itinerary and print a BP. This is much more variable as it relies on various settings being configured, but there are definitely airlines where it will work.

Scenario 3: Where staff at airports don’t use airline systems but rather their own (or that of a handling agent, e.g. Swissport), the agent will be able to select an alternative flight and print a BP fairly easily. These are easily identified on BA because they’re the ones where online check-in isn’t available and local BPs are printed in a non-standard format, e.g. NUE, DBV.

Scenario 4: Where staff at airports are employed by a handling agent and at different times of day handle different airlines’ flights, they may (if suitably trained) have logins for more than one airline. They could potentially log out of one system and into another to access a BP.