Sounds as though your problem is getting a high enough gear to give you more speed. So your 11/28 -7 speed cassette will not give you a higher gear just by adding more gears. The 11t gear is going to be the "Fastest" you can get.
But it is possible to put a larger chain ring on top give you higher gearing. Not certain what gearing you have at present- But if it is an older style you probably have 48/38/28 chainrings fitted. A trip to the LBS will confirm but it is possible to get higher gears for most chainsets.
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How long was I in the army? Five foot seven.
Spike Milligan