I don't think you can apply to a college with an I-20 of some other college. But there might be loop holes you never know.Yes you can come to US months before college starts and look for another cheap college but if she doesn't register in that perticular college for which she got the visa the college might inform the immigration and she might be out of status. But as said, if the accepting college issues and can prove USCIS that she is a full time there and provide her status there might not be a problem. You might want to consult the International Office of the cheap college to be more accurate and or a lawyer.

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