I don't know what the procedure is with BRPs now...
I came in on a fiancee visa, so didn't have one at first. After we married, I got my first FLR(M), and had a BRP with that. I submitted that BRP to UKVI when I applied for my second FLR(M). I got a new BRP with my second FLR(M) approval, and I submitted that one when I applied for ILR. After ILR was approved, I got my third, and final, BRP. I held on to that one until after my citizenship ceremony, then my husband and I ceremoniously cut it into several pieces, I wrote a note explaining I no longer require it, and I sent the pieces to the address in the letter. It was scary and satisfying at the same time.

I never had more than one BRP at a time, and there were times when I was 'between visas' when I didn't have a BRP at all. But, as I said before... I completed everything two years ago. There have been
so many changes since I did it. :/ I wish I knew more about how it's going now.