mechBgon is absolutely correct that you'd have to do some serious mods to the rear to get 8 or more speeds.
Here's some excellent info on those hubs and how to remove the cassette:
Shimano Cassettes & Freehubs
I think the most economical solution would be to salvage a triple setup off another bike, and re-install that triple crank, bottom bracket, front derailer, and maybe shifter onto your 564. Look for an 80s touring bike.
Do you have a local bike co-op to consult or search for parts? A local bike dude? A guy with a huge pile of bikes in his garage?