Short answer: yes there's no legal reason why there couldn't be a pTO and a PTA in the same school.
However, I don't really think it's a good idea for the long term. It unnecessarily confuses the heck out of parents and creates two infrastructures (and communications systems, etc.) where only one is needed.
If there's an unsupportive principal or parents who don't agree with your stance on things, starting the PTO and operating it aside the PTA won't change those things.
My opinion: better to work to create change in the existing parent group. It can be frustrating if the powers-that-be really like being the powers-that-be, but it's worth it.
I feel for you, I just went through this myself. I had to search myself and decided to move on to help people who want my help. I'm doing little things for that school, tomorrow I'm selling summer grams for 1 hour. And I will help and bookfairs and in my sons class. It is heartbreaking to go from President to outsider in a years time, but if they want to do it their way let them. It seems our PTA has been taken over by a prayer group. They broke every rule in the nominating rule book. But, I truely wish them well, in their own demise. LOL Good Luck to you.
Our PTA has run amok. Total disregard for bylaws. Employees hand pick officers.When 2/3 majority of members at Annual Mtg. forced a valid election according to bylaws and RONR, principal and outgoing president held a second election.Principal refused to recognize the first election and only announced the results of 2nd election.Appealed to state PTA who opted to let the principal decided which outcome she liked better...Hmmm, her handpicked officers, or the rebel parents? Our membership is very low, in fact at one point there was more faculty than parents. I can't get faculty to drop PTA, but what about wedging in a PTO?