More than not my same day international flights are a combination of 2-3 different tickets, airlines etc.

Even if those airlines are not in the same alliance (my example: Swissair versus StarAlliance-members) checking-luggage through is NO porblem, 'only' boarding passes must be asked for at the connecting (transit-desk or lounge) airport. If the two or three tickets are with the same airline I never encountered any problem to check-through from start to end (and very often I combine two tickets from UA: a transatlantic-one in combination with a UA-'visit-US'coupon'-one).