I see that self hosted RSS aggregators usually provide a web browser interface for all the subscribed feeds. What I'm looking for is a self hosted option where I can use my feed reader application with it...so I have the flexibility to look at all sources or specific sources and individually handle read status, starring, etc., the flexibility to read things when offline after syncing with the server.

I want the feed reader interface to be as if it's subscribed directly to the respective feeds (though it would be subscribed to feeds on this self hosted service).

Is there anything like this? It sounds more like an RSS Caching service than a feed aggregator.