Yes, but.
You could make your loggers named with the class + user involved, rather than just the class, and create the logger on the method (or if you want to get fancy, cache loggers in some kind of pool keyed by user), and then configure logging appropriately.
It is very messy and intrusive to the code, but since the user is a runtime property, I don't see how (short of AspectJ or its cousins) how you avoid that kind of mess.
Another option is to specially format your log messages and include the user name in the log message, and then parse the logs afterwards. This would enable debugging for everyone (which may be a performance issue, obviously) but if the concern is more about isolating a users logging rather than limiting the amount of debug calls, that may be a solution.