Furry stuff, oekaki stuff, and other stuff.
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That requires adding a new table to the database and writing a multi-table query to group types together. It's not hard, but it's not so trivial that it can be added without knowledge of database queries, especially if you want to have a clean interface allowing people to add custom categories. Also, it's not really a good idea to add that feature to the registration page. It should be part of the profile editor.
I started working on that a while ago, but the profile editor is already so messy that adding even more fields made me uneasy. I'm not sure I'm interested, given that there's not much point continuing work on the BBS unless a good HTML5 paint applet shows up so I can replace the aging Java applets.
Like, additional website fields, a spot where people can put what usernames they get on in-game, additional gender options, etc. That sort of stuff.
That depends what kind of information you'd like them to provide. Some additions may require the database to be updated, and some may not.
How would one go about modifying or adding fields for users to fill out on the registration and/or profiles pages?