I would do it in the manner of, the 'points' you acquire to upgrade stuff, gets acquired for all characters. You use them per character differently. You may need to reconsider how much payout each point giving event gives though.
Like an RPG where all characters receive the same amount of EXP regardless if they're currently active in the party or not.
In my opinion, I don't like having X and Zero 'share' the same EXP or SP to upgrade their abilities. I think X and Zero had level up on their own and have those points to themselves to upgrade their abilities because you're using them and gaining experience with them when defeating the enemies so it makes sense that character gains the EXP, not both and it allows more freedom and choice for the players.
They're not in a 'party' per say and plus it's also the player's decision if they want to use the character more so than the other (though I'll be playing both X and Zero in this game) and I like to have max characters for the ultimate level of fun after clearing the game or wanted to test them out. Plus if the SP is shared and I want to use a maxed out X (or max out what I can with the maxed amount of SP) I have to downgrade Zero's abilities so I can upgrade X's which is quite annoying in my book if I swap out a character with low health right before the boss and my other character is at full health but weaker abilities instead of having him already powered up and switching out so I don't have to worry too much... though it does make it challenging for some players, but for others they like to be ready with a fully-equipped character.
It's sort of limited with the freedom of which character you like to play as the most, as in X4 you can choose which character you want to be and gain upgrades for that character only (though you cannot change characters after this). I don't mind sharing the Heart Tanks as I like to even distribute them between my characters. I also enjoyed X8's character customization with the upgrade parts with the Metals and I like to alternate between the three characters with ALL the abilities maxed out for fun, even if I use Axl more than X or Zero I like to go back to the old X and Zero team for ultimate carnage with their maxed skills.
But if you're going to have X and Zero share their SP then go ahead, I'll just max out one of the characters I'm going to use the most that way and do a New Game (or New Game Plus if there's one) with the other character.
Good luck with your project JKB!