Join Date: Feb 2005
Bikes: Trek 5500, Colnago C-50
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To change to an 8, 9, or 10-speed cassette you would have to replace the freehub or complete hub, shifters if indexed, and chain to match the cassette. The cassette needs to match the shifters. This would be a considerable expense.
You can probably find a replacement 7-speed cassette (or freewheel), the size of the cassette (number of teeth) should be chosen to compliment the terrain you ride, hills or flats. With a new cassette you should probably replace the chain. You can use a 7, 8, or 9-speed chain with the 7-speed cassette.
Be careful to not spend more money on components than the bike is worth.
A good source for general information is: http://www.sheldonbrown.com