I don't think Frodo could have become a wraith like the other Nazgul; he would definitely be a lesser wraith, possibly even a spy because of his short stature.
You have to remember that before the Nazgul were wraiths they were great kings of men, skilled in battle and strategizing. It would be hard to find another living person who would meet their skill. The Nazugul were use to working with each other, they could act as a team, and a new addition to that team may have caused friction between them. Maybe this is why they didn't have more Nazgul, but I think anyone would be content with Nine wraiths.
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I heard the bells on Christmas Day. Their old, familiar carols play. And wild and sweet the words repeatof peace on earth, good-will to men!
~Henry Wadsworth Longfellow
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