if we use the transitions:

q1 (epsilon , epsilon -> epsilon q2) (epsilon , epsilon -> epsilon q3)

we create 2 branches, one with q2 and one with q3.
after the split they have their own copy of the stack, my question is:

is it possible to have a final accept/reject based on the accept/reject of the 2 branches?
Can I make it such that the final answer is accept only if both branches reach the accept state?

one way to solve this problem would be to have a PDA with 2 stacks.
Is it possible to simulate a 2 stacks PDA with one 1 regular PDA with one stack?
I know that a 2 stacks PDA can be simulate with a TM, but can it be simulate with a regular PDA?