This guy and several others have already stated why this isn't going to be possible. Not only that, you're misunderstanding the issue at hand. Yes, there can be multiple Smash Balls appearing in a single match, but there will... and here's the stresser..never be more than one active at a time.
I'm not saying that I think two Final Smashes can be active at once, but I think it's absurd to say that having two at once would automatically introduce glitches. The programmers do a very good job of ensuring that such things do not cause glitches; Final Smashes aren't really different from any other move in the game in that regard.
Of course there are other factors to consider when Final Smashes are involved. So far the biggest evidence I've heard as to why it isn't possible is because of Snake's Final Smash, but even with that I'm sure the programmers could come up with some way to handle it.
I'll say most likely only one Final Smash can be active at a time, but I'm not sold on the idea. I think it's interesting then, that one way to try to prevent the pity Final Smash may be to try to hang on to the Final Smash for as long as you can when you get it. This could especially be true for characters whose Final Smashes aren't as good or aren't appropriate on a given stage (for example, you may not use ZSS's final smash if you don't want to change back).