You can do either. There are pro’s and con’s.
I have done it both ways. The main reason I chose to do a different supplemental than the main work was that I found I recovered better not putting too much strain on one particular muscle group in one session. Also being able to switch it up makes BBB a little less “boring”. Of course there is the extra setup/warmup time but honestly you will already be warm from your main work so it shouldn’t take you long to warm up to a 40-60% TM.
On the flip side (this is purely my opinion from experience) I feel you don’t get as much as a hypertrophy effect from doing a different supplemental lift. The muscle fatigue isn’t quite the same.
Once I adapted to the volume I ended up doing the same supplemental as main work as recovery was no longer an issue. Just look at your current work capacity, strength levels, and experience and decide what is best for you.