most of us prefer vintage bikes, so most of us will tell you to keep the "heart" of what you have (the frameset) and up-grade the components. Depending on what new gears you desire, you may have to spread the rear to accept a wider spaced rear hub (ie: you probably have 126mm and next step up for 8/9/10 speed is 130mm) and this "cold-setting" can be controversial amongst us C&Vers. If by "more gears" you want a triple crank to replace a double, the process does not involve any frame alterations, and you can keep the FiR rims you like. In either case, I assume you'll want brifters to go with the new drivetrain, and most new ones are very pricey and only 9 or 10-speed. If you want to keep 6 or 7 in the rear consider barcons (indexing if you wish) and nice conventional brake levers.