Gregory's Server
What's the appeal? For one thing, you'd be able to connect to all of these services from the same account, rather than setting up accounts on multiple instances running different services, or compromising on an instance that kiiinda does most of what you want.
But it would also let followers pick and choose which streams they want in their timelines. Maybe they want to read your thoughts, but don't need to see your checkins. Maybe they just want to see the links you post. Or the photos.
The most interesting way to go about it, I think, would be to prioritize breaking forms of interaction down to very basic forms. Most social media services are highly hybridized — post text, photos, videos, polls, checkins, etc., all in one place! Since this would be a modular server structure, the services don't have to be hybridized. Each could focus on being really singularly good at letting people do the one thing the service is most about.