The shelves won't sag.

One shelf is not going to hold enough books for it to sag.

Methinks, that, perhaps some good culling and eliminating may the first order.

I have a friend who took the Billy shelves to the next level and bought some of the glass doors for his and they appear to be built in.

Sad, though they house his collection that he enjoyed collecting all of these years, he is no longer able to appreciate them due to severe health problems and getting old. He says that they bring him no joy anymore. Rather, they sit there across from him in the room and seem to almost mock at him that these are all a thing of his past and that he has no good home for his collections to go to. He is facing end of life issues.

Maybe it would be good to pare them down a bit and find the pleasure in the ones of most value.

That is always my advice to anyone when they ask about storage. I firmly believe that is best to first start with a honest reckoning before you begin to look for places to store stuff.

But, no the shelves should not sag because any one shelf does not hold that many books unless you really stuff them in there or pile them up densely. Then, you might have a problem.

And buy an extra shelf per unit for more storage.