Maybe. There is nothing at the NIC level to prevent you. However the individual fraternities might have requirements that you have never been in a similar type of organization.
__________________
And he took a cup of coffee and gave thanks to God for it, saying, 'Each of you drink from it. This is my caffeine, which gives life.'
There are lots of regional fraternities and sororities at the SUNY schools. They have a long tradition there but I don't think they would fly elsewhere.
To the OP - yes, you can pledge a fraternity at FSU. I would let your current brothers know you are doing so, just to be courteous.
__________________
It is all 33girl's fault. ~DrPhil