If you have two sound sources creating the same sound at the same time/amplitude/etc, there is of course a large change of cancellation. Wave cancellation is when waves of equal energy collide in such a way as you effectively dimish their energy. You can have cancellation without the sound waves being completely cancelled. Some freqs will be diminished, some may even be amplified due to wave reinforcement (same freq/amplitude waves close enough together to reinforce each other, opposite of cancellation).
The bottom line is the result will be an uneven frequency response, and one that likely will be all over the place. An EQ could adjust for it somewhat, but not completely.... and I really dont see the advantage of trying to do it.
You are simply trying to reproduce a bandwidth of frequencies accurately. A sub in a sealed enclosure gives a nice smooth flat response along the entire bandwidth usually, where as a ported box peaks output at a certain point, dropping off drastically below but remaining relatively flat above this freq (why low tuned boxes can have excellent SQ, contrary to what some people believe). So, why add another speaker of another size/brand/whatever that's going to complicate things?
What exactly is the purpose of wanting two 12's AND one 10 to play the same frequencies? If its to make it louder, you'll likely be louder with the two 12's alone. Certainly would be louder with three or four 12's instead of two 12's and a 10. So if its to make your stereo louder, that's a bad idea.
If its out of convenience (you already own the 12's and 10), Im sure you own a portable boombox too, why not strap it to the dash and have those speakers making noise too? Because as Im sure you already know, it would most likely hurt the over all sound performance, not help it. The same is true of mixing sub brands/sizes/models, it simply will not help the SQ performance. Just because you own it, and it makes music, doesn't necessarily mean it will help your car stereo's performance. So if its to make your stereo sound better, that's a bad idea also.
The only real way Ive heard of mixing sub sizes effectively was with a fairly compex xover setup so each sub size played its own frequency band. But you also have to consider how well each sub will perform in its particular bandwidth, how well they will blend together, the transfer function of the vehicle and its huge impact on the sound, etc. Things get very complicated, and after all is said and done, I still find myself asking .... why do it anyway?