Modern Sonic spends quite a lot of time in his levels in 2D. I've found a few useful moves that can be applied in many situations, and I figured I'd catalogue them here.
Stomp-Jump: Stomp and then jump immediately after, canceling the stomp cool-down. Can be finicky based on which surface you're doing it on, but most allow this method. Much faster than waiting to land and then jumping. Useful for ascending platforms where not much lateral movement is required, such as strings of them against walls (e.g. Laser Cannon 1, Plasma Cannon 2). Probably the easiest tech to execute consistently. EDIT (1/28/18): This move is ONLY quick if a horizontal directional input is registered at the time of the jump, otherwise it fails to cancel the stomp end-lag and actually lengthens the process.
Stomp-Slide-Jump (SSJ): Stomp as close as possible to the edge of a platform, immediately slide in that direction, and jump as soon as you're sure you've entered the sliding animation. This gives you an immediate burst of speed without having to take time to accelerate. The drawbacks to this: I'm fairly certain it doesn't give you top speed, I'm fairly certain it doesn't allow you to accelerate in the air after performing it, and it seems that the higher you jump, the more you lose speed in the air. This has worked on every platform I've encountered in the game, and is especially useful in Fire Cannon 2 and Modern Sonic's Vanish Panel. EDIT (1/28/18): Can also be done without the initial stomp (though the stomp is very helpful for positioning).
Boost Hop: When you air boost in this game and already have upward momentum, the boost has a slight "hop" to it that allows you to gain extra height and distance. From what I've experienced and seen, this can be attained at any speed. Personally, I've found that it's easier to pull off if your horizontal speed is lower, because I have trouble executing it when moving faster. That, though, seems to be just a personal problem, since I have seen it done at top horizontal speed. When used after the double jump, it can yield some incredible height. This move is particularly useful in Plasma Cannon 2. EDIT (1/28/18): This move seems to only work if not boosting for the initial jump.
