Saints row 2 does exactly this and oddly enough seems to be the only game that did this. I enjoyed it, it is a shame no other game has implemented a similar system since.
I've never played one of these games since I thought it was a "more of the same" game if you were already in to GTA. I actually want to play the PS2 exclusives of GTA again. I think they were ported to Vita so I could emulate fairly well even on my laptop.
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