Historically, the five Solae have been a divider between Catholic and Protestant theologies. Yet, I can't help but notice that most denominations do not believe in the "alone" taken in its fullest sense. For example, The Methodist church does not believe in sola scriptura, but instead prima scriptura. Are there other Protestant denominations which reject some or all of the solae?
You're correct that Methodist don't accept sola scriptura, but instead prima scriptura. Not only that, they also reject sola fide. That is because they teach synergism. Now, I do know some Pentecostals also hold to synergism, and therefore reject sola fide. Also, if you consider Anglicanism to be Protestant (which most don't, but they are related) there are multiple opinions among them. They're seperated between high church, broad church and low church. Each tradition gets either more Protestant or Catholic in its theology. Now, rejecting all the solas would probably disqualify you as a Christian; sola gratia (grace alone) is something all Christian denominations teach regardless if they are Catholic, Protestant, Eastern Orthdox, etc. Ultimatly, with the 40,000 different kinds of Protestants out there, it can get really diverse.