Replacing Cam Nuts and Locks on Store Bought Furniture
Check the "Cam Connectors" (that's what the stores call them). They can rip or split &amp; not provide a solid connection. If there are gaps &amp; the panels aren't sucking together tightly, then you'll need to back out your screws/pins.

The screws/pins do hold everything together yes. But, the other thing they do is splay-out the screw receiver in the drilled hole to firmly anchor the screw/pin. If screwing isn't getting them flat, then you can hammer the balls at the bottom with the head end of a nail or a nail-set or a bolt or rod.

This will let your screw/pin sit at the right height &amp; everything will snug-up beautifully. I wouldn't install through-screws unless they aren't visible. One final suggestion is to take it all or mostly apart &amp; apply wood glue to all seaming panels. This will stiffen the entire piece incredibly, but you won't be able to take it apart in the future.