For example, I compose in Musescore. I record bass and piano myself but my skills (and budget) in recording and mastering are rather weak.
It sounds like you are looking for a website that allows you to submit your work and combine with other people's work. I know of two websites that allow you to do so.
Here you have two options:
Start a Project and set restrictions on the type of content by making a
a) Private Project - Where you have to invite people to make changes
b) Public Project - Where you allow anyone to add their ideas (with the power to choose who makes the final cut of course.)
Write and upload music with the intention of completing someone else's project.
There are three accounts you can register for and all of them are free. There is also a leaderboard that tracks whose composition has the most popularity.
This website operates very similarly to the first, but it has a brighter interface to it. The main music here is Singer/Songwriter, Country, Pop, Rock, and Blues
Hope this helps.
Another possibility is BandHub. This probably isn't quite what you're looking for, but it's essentially a multi-track youtube, with various people able to record & upload new video tracks to a song. It's focused more on recording, than on composing, arranging, mixing, or mastering.
My experience is that it's not so good with the post-production & editing side of things. For example, AFAICT, it doesn't really give you a chance to edit what you record before uploading; once you've recorded a track, you either upload it right then, or you don't. Of course, it's been a while since I've looked at it, so things may have changed.