TiddlyWiki provides a non-hierarchical notebook with a beautiful interface. I highly recommend it. It's based on small notes or tiddlers that you interlink with hyperlinks and through tagging. Instead of long articles with many headlines, you try to build a web of small notes that all contain hyperlinks for more info. Especially the Node version is good, because it stores your notes in plaintext files inside a folder so you maintain control (as opposed to them being hidden in some self-replacing HTML file).

But it is a personal notebook. You can host the Node version on a server and grant people write access I believe, but it isn't meant for that, it's a hack and people have reported bad experience with that. There's also a paid, hosted option provided by TiddlyWiki itself but then you aren't in control.

This isn't about the technical details of a hosted TiddlyWiki but rather the structure behind content. Wikipedia has articles on topics that people contribute to, and the live version is highly editorialized to ensure it doesn't get filled with crap. Tiddlers work fundamentally different. People jot down individual ideas and connect them. But everyone has their own approach to or information about some topic. Let's say birds. I have some observations about birds that I could store in ~larry/birds.tid, while Jason writes ~jason/birds.tid. Some of our information is objective and universally relevant, while some is personal. Now, a canonical article about birds could be created in canon/birds.tid. TiddlyWiki supports transclusions so the information can be grabbed directly from my and Jason's .tid files individually, not just via copy/paste but in a live updating / mirroring way, and the option can be provided to read a given section in its context on the personal tiddlers. That way, multiple people can keep track of their own information in a way that doesn't conflict, objective information can be served in canon/, and users are free to explore the more obscure information for themselves without senior editors removing the information like on Wikipedia. There can even be equivalents to canon/ for different communities, all with their own arrangement of information.

Once again, the actual TiddlyWiki isn't so good for something that's collaboratively edited; I brought it up for its lovely interface but this implementation would require a fork or clone, I think. As far as existing software goes, there's DokuWiki which has the advantage of storing the data in plain text files. It's also extendable and provides a decent feature set. For something simple I'd recommend that. If you want to deal with databases, then MediaWiki seems like a good option.