If the mattress is saggy or not firm, it will not be a good foundation for the second mattress which will sag in the same places. Better would be to get slats

Yes,but it will be totally unstable. It will not stay put, but slip around unevenly.

My old box spring is falling apart. My mattress is still ok. I have been looking at new mattresses, someone suggested that I can just use my old mattress as a box spring? I've asked a few people and they don't see why not. Opinions?