It was over a year ago that I did this, but I checked two bags in for the route TPE - HKG - LHR - AMS - BSL, with AMS-BSL on KLM. The rest were all bought through BA although as the TPE-HKG flight was on Cathay so that's whose check-in desk I used at TPE.

Interestingly, I checked in two bags (1x30Kg, 1x20Kg) and was worried as the AMS-BSL flight was KLM economy, but it proved no issue.

I got an sms while in AMS saying my bags didn't make the LHR-AMS flight despite having a 5 hour transit at LHR. I did try to get both BA and KLM to send the bag from LHR to BSL (in which case it could have beaten me as I had another 5 hour transit at AMS!) but they said the bag had to fly the original route. I got them the next day. The bags were quite heavy so having them couriered to me saved me the hassle of getting them to my place from the airport in BSL.