Just to reiterate from my recent experience: through-checking a bag can be difficult on multiple IB tickets. I was informed this past weekend that since I had already checked in for my onward segment, they could not tag the bag through, and they could not figure out how to undo the check-in. I'm not sure if that was really the case, but the employee (a contractor at an outstation) seemed knowledgeable enough and tried for at least 10 minutes to force it though.
In the end, my first segment was severely delayed, ran from T4S to T4 to try and get my bag from the conveyor, which hadn't even been turned on after 20 minutes of waiting, before I gave up and dashed back to T4S. Still don't have the bag.
Moral of the story, leave yourself plenty of time in case things do not go as planned at the airport.