Not in any way that would be officially confirmed by FD. But you can (actually, will) support or hinder them more or less directly by every move you do in the game. This is usually called the BGS (background simulation/story), and sort of an endgame - especially since FD never told us the rules, so we had to infer everything on our own.
For starters, you can do missions for them. As long as you don't fail them, every mission you do for them will strengthen them - they will gain influence (INF) in the system you do those missions. With some missions, you can choose to give them higher INF at the cost of a lower payout for you.
Depending on what you want to achieve, though - be careful. Once their INF level crosses paths with that of another faction in that system, those two factions will go into conflict. Depending on that faction's orientation, this can be a (civil) war or an election, which can be won or lost. Winner takes usually one base/settlement from the loser (if available).
If your faction is on top of the heap and gains enough INF, they will try to expand into a neghbouring system that isn't completely booked. If they're on the bottom of the heap and lose too much INF (and are not a faction native to that system), they can be booted out of the system.
There are other means to steer their INF up or down (down is harder to do) or to push their expansion into a desired direction (hard to do). The smaller the system's population, the easier it is to swing it around. The less other CMDRs are doing random stuff in "your" system, the easier it is to swing around. And a few systems and bases are lcoked out of this BGS game by FD.