If you want to keep the drivetrain 3 X 7, you can easily do that (low level parts, but they`ll function as well or better as what you have now), or you can go whole hog with a zillion Dollars worth of high end 10-speed parts, or anything in between. The only thing you won`t be able to do without frame mods is convert to disc brakes, although you could switch from straddle cantis to "V" brakes as long as you replace the levers at the same time.
EDIT: If you go looking for replacement or upgrade parts for anything, note that an unknowledgeable or unscrupulous vendor or LBS employee might well tell you that you can`t do this or that. You`ll be doing yourself a big favor to research "speeds", cable pull, hub width compatibilities and work arounds for yourself before starting. Sources such as Sheldon Brown, Park Tools, or Biketutor will give you all you need to know, or you can just ask on the mechanics or collectors subforums here on BFnet or any other big cycling discusion forum. People will gladly explain exactly what you can or can`t do for any stage of a refurbishing.