No.
In the main series, all living Saiyan-blooded males following the Frieza Saga manage to reach at least the first level of Super Saiyan. Akira Toriyama's reason for never having any female Super Saiyans was that neither Pan nor Bulla had the incentive to transform, and that he never drew female Super Saiyans because he couldn't figure out what they would look like. The Dragon Ball GT Perfect Files implies that Pan has the potential to transform and might have become a type of Super Saiyan never seen before.
It is unknown if there were Super Saiyan females before Planet Vegeta was destroyed as Fasha is the only full-blooded female Saiyan seen in the series.
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No.
well, actually no there isn't. but considering that that dragon ball z waz written by a human on earth the conclusion tilts more to saying they arent real. since there probably waznt any planet vegeta to begin with that means there are no saiyans. but it would be sooooo cool if trunks, vegeta, and goku were real wouldn't it?! i love saiyans (especially trunks ^ ~ )!!!!!!!Ok im sorry for popping out of no where but i have an answer.. I can answer any saiyan question because i know of a few(and am one myself) Even though it was written by a human it was a legend before he wrote it there was an old japenese legend of super saiyans so he took that..
Yes there are but not that many
no that wouldn't b possible... unless all the saiyans fused but still.the highest it can go is Super Saiyan 10. but that's only in Dragonball AF. normally its only 4
because he knew that the Saiyans were getting stronger everyday and he couldn't control them. He was also afraid that one would become a Super Saiyan and overthrow him.