Can I work on lots of working copies from different repositories at once?

Yes, you can. This is a standard feature of Subversion. Each directory which was checked out of Subversion remembers where it came from. You can even multiply select working copies which came from different places, and update or commit them all at once.

If you want to have different subdirectories to come from different repositories you can set a special Subversion property called svn:externals.

Please look at the chapter External Definitions in the Subversion Book.