I put new 3x10 Deore shifters on my MTB, a 10sp wide cassette and XT derailleur, but left the older 3 ring 7sp crank on. No problems whatsoever until I realized the big ring was shot. I replaced that and no further problems. This is all Shimano, where mostly everything stays compatible.

A 3x7 setup gave you 21 gears and maybe 17 were usable without cross-chaining. A 3x10 gives 30, but I can't remember the last time I went into even the middle ring, never mind the small, and I don't worry about cross-chaining in this setup. A 2x12 gives 24 and there are probably more useful gears available using that than either of the others.