Would it be possible to SOC the following animation?

What I mean by this is, would it be possible in a SOC to make it so that you basically do a no-spin jump, but inbetween the Springing and Falling animations, it plays the spin animation one/two times?

Maybe. You know that SOC are for make things or edit things, but for chaning animation I think you could change Sonic in some Char Editor. (Bad answer)

Not in between, but you could make a few extra frames to go to first, before the falling.

Yeah, all you'd need to do is set the first falling frame as the first spinning sprite, set 3 freeslots to be the other 3, set a fourth to be the first falling frame, have that frame go to the 2nd falling frame that's already set, and then have that frame loop to the fourth freeslot. The only problem would be that any SOC you add that uses those 4 freeslots will screw up your character :P

EDIT: I think you can make it that the spring frame can go to the spin frames after a second or two, for a spinning-in-the-air effect to be more improved. It might be a little weird with the animation, though.

It's funny because I actually did this back in 1.09.4. It was a bit buggy then though, and I don't particularly care to port it, but if you're interested, it should work something like this:
-PLAY_FALL1 (I don't remember the numbers) should have its NEXT state set to a custom frame. (Freeslots if you don't want to break anything) Change the spritesubnum of this so that it shows the "falling up" frame (I THINK that would be found in PLAY_PLG, but I forget.)
-These custom frames should be a loop of the spin animation (See PLAY_ATK for the spritesubnums you want). The last frame should be a copy of the original PLAY_FALL1, with its NEXT state set to PLAY_FALL2.
-PLAY_FALL2 should have its NEXT state set to that copy.

There might be something horribly wrong in there, but I think that'll get the effect you want when the player is nojumpspinning.

Draykon said:

Change the spritesubnum of this so that it shows the "falling up" frame

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Correct me if I'm wrong, but I thought spritesubnumber set the attributes of the sprite, like what level of transparency it had and weather or not it was unaffected by brigtnesss. o.o

Hyper Shadic X said:

Correct me if I'm wrong, but I thought spritesubnumber set the attributes of the sprite, like what level of transparency it had and weather or not it was unaffected by brigtnesss. o.o

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It does both, AFAIK. But its main purpose is to select the frame to use.