"How can I build my character to take advantage of charisma as much as possible?"
Short answer: you cannot further build your character mechanically (except for one Edge from Slipstream). By design, Charisma is of limited, non-combat use, but where it is used it is very powerful.
Long answer: to get to +10 Charisma, you've already maxed out all of the Charisma Edges and taken a Race with a Charisma bonus (the Valkyria race from Slipstream combined with the Attractive, Very Attractive, Charismatic, and Noble Edges from the core). You've already super-specialized your character in that direction (spending several Advances to do so) and there are no more Edges that can boost it.
Charisma is intentionally limited in that it only works for two trait rolls: Persuasion and Streetwise (and a successful Persuasion roll raises the result on the NPC reaction table; two with a raise, but it's capped at that). These are both non-combat rolls. What this means is that you are really, really good at convincing people of things and chatting around to find out information and that general people will always be Neutral or better (the GM can still of course ignore the NPC reaction table and just have someone be hostile. You still have enemies). But aside from boosting your Persuasion and Streetwise, you've more or less maxed out your ability mechanically. You are essentially a well-liked superstar who can get their way whenever they want.
Realize though that there are limits to a high Charisma. Although you can probably talk a great deal on price or get someone to reveal information that isn't common knowledge, having a high Charisma does not equal mind control. No matter how well you persuade someone, they won't let you into a classified building if it means they'll lose their job. More importantly if someone wants to kill you, you might be able to convince them to stop if they are unsure of it, but not if they're hell-bent on killing you, no matter how charming you are. And that's the major limitation: being attractive and charismatic is helpful in social situations, but doesn't matter if someone is trying to kill you. Again, this is by design (and it's how it works in real life).
There is one Edge from Slipstream that you can take that would help fill in your combat weakness. The Femme Fatale/Ladykiller Edge lets you use Persuasion (modified by Charisma as usual) as a Test of Wills during combat. Like other Tests of Wills, this will allow a +2 to your next action against them and possibly Shake them (but not wound). This will help you set up for an attack or aid your teammates, but it won't completely get them to stop. There isn't anything in High Space that modifies Charisma, Persuasion, or Streetwise.
So to sum it up, you're at the end of the line with your high Charisma character. Except for the Femme Fatale/Ladykiller Edge, there is nothing more you can do to build your character, so you will need to get creative and find story reasons for how such a high Charisma can be helpful. Also, it's time to diversify and fill in the weaknesses you've left by spending so many Edges on boosting Charisma.
Finally, I'd recommend talking with your GM about your character. If you were running that character in my game, I'd have a hard time challenging you with a +10 Charisma because you'll blow through most every social situation I try to throw at you and honestly I'd be concerned about that making the game not fun (after all, what's the point of running them?). Savage Worlds isn't really a min-maxing game like D&D and I'd instead suggest that, for the fun of the game, you retrain some of your Charisma-boosting Edges into something else so that I can still make social situations a challenge you.
Or if you insisted on keeping it, I'd make your high Charisma a curse. Like give you an annoying fan who always follows you around, even in combat. Or make it so that people stop you to get your autograph when you are trying to get away. Or have the tabloids telling all sorts of stories about stuff you supposedly did. Just saying, in the hands of a vindictive GM, high Charisma is a curse!