I obviously need to brush up on my American History. But there was a "State of Franklin" that existed for a year or two (even if not recognized by the federal government). Also, my wife's ancestor was one who signed a petition to form a new state from Southwestern PA and northern MD. I never have seen the name of the proposed state. Time period was about 1780.
In Oklahoma, which has a much more recent history, we had several parts of counties that wanted to join together (secede from the counties they were a part of). The process required petition to the legislature, a census be taken, and a vote of the people in the affected counties. Rarely did such a change pass the vote.
Mahlon Erickson