Far as I know, the major calendaring protocols all use HTTP as it is. Do you just want a mediator/self hosted backup? Or do you want to host your own calendars?
If it's the latter, Radicale is awesome.[1]
If it's the latter, Radicale is awesome.[1]
Pulling raw iCal data over HTTP is possible but if you say, set up a recurring event several months back, you need to fetch that original event (even if it recurs every day) to include it in your calculations... I'd love a self-hosted version of this Nylas API [0] for example.
We are evaluating if it may be interest on it to release as a separate SaaS.
You can find my email on my profile if you want to discuss further your needs.