In order to help give Mega Man X a mechanical identity separate from Mega Man other than "Mega Man, but bigger and/or more aggressive", one thing they could do is implement the Variable Weapons System (or whatever Mega Man X's variant is): His Neutral or Down Special would allow the player to change what weapon he has equipped for his Neutral Attack, Forward Tilt, Neutral Aerial, and Forward Smash. By default it would be the X Buster that works similarly to the Mega Buster, and his Forward Smash would fire a Charge Shot, and you would be able to swap it out for one of 2-4 other weapons, each with their own energy bar that depletes as you use it. If you run out of energy for that weapon, you can't use it until your next stock or something.
For a example of what a Maverick Weapon would be like, I'll go with Storm Tornado. With it equipped, your Neutral Attack, Forward Tilt, and Neutral Aerial become a multi-hit horizontal tornado projectile that travels straight forward deals a lot more damage than what can be expected with the X Buster. The tradeoff is that you can only have one shot on screen at a time. Your Forward Smash becomes a vertical wind pillar that forms around you that extends quite high above you, and low below you, but only goes through semi-solid platforms when extending downward so as to not be way too powerful as an edge guard tool.
EDIT: They wouldn't all have to be "buster replacement" style weapons, that would be really boring. Storm Tornado is just the only weapon I'm familiar with that wouldn't have significant issues upon implementation since I've only played through the first game so far.
Because this mechanic would require pallet swapping Mega Man X to show what weapon he has, he would have to have alternate costumes instead of pallet swaps*, which could be based off of the various armours seen throughout the games assuming there are 8 of them.
*I know Mega Man takes on a new appearance for weapon swapping in Mega Man 11, and that would work for him in Super Smash Bros., but I don't think that'll ever carry over to Mega Man X because of those armours, so this is probably what the workaround would have to be.
They could even amalgam the designs like they did with Snake (although it was two different characters in that case). Probably the least likely option, but I would think it's still in the realm of possibility.