Multi-faceted website -- is the Theme switcher a solution?

*** This is not a support _ticket_ sensu stricto, as nothing is broken. But I have an idea and do not know how to implement it (I am no coder anymore, since Framework V ) so I need some advice. Please feel free to move this post wherever it fits better than here. ***

My website has now two, soon hopefully three functions:
1. A "safer social network" for volunteers involved in refugee support in Europe, run on Buddy Press.
2. Technical and inspirational hub with several services for the same population: fundraising, open tech documentation, news aggregation, (planned) MailPile-based email, etc etc.
3. (funding and IT support volunteers permitting) A multisite "colony" of blogs, sharing services, connected to individuals and groups.

BTW, none of that would be possible, without your marvelous products, folks. And without my friend, who decided that he rather pays for my subscription than suffer constant nagging from me.

Now, my dilemma: As the site has three various "faces", ideally I should have three various templates (technically it can be one, configured in three or four ways), available for users to switch between.
A neutral one, with a lot of information "About us" for a first-timer. Say, twenty sixteen.
A community one, focusing on BuddyPress and its functionalities. Say "BuddyPress Community"
A hub-ish one, more into services and information.
A multisite one, presenting a wealth of sub-sites with relevant tools.

Of course it is not just about selecting and switching between themes. It is also about their configuration. Various sets of menus, widgets, different texts etc. etc. Customization and its results, stored with the template concerned, available to be retrieved when switcher selects it.

It seems that this is beyond functionality of this plugin ATM. Or am I wrong? Perhaps there is some way solve it? Using different child themes from the same root? AND the switcher? I know too little about the intestines of WordPress, so hopefully someone will give me some hint?