Pushdown Automata - can you have multiple transition functions options between 2 states? I was wondering if you have 2 states, lets say q0 and q1. Are you allowed to have multiple options to transition between these 2 states?

For example,

 - if you have a 1 and the stack is empty, push it on the stack, and transition to q1
 - if you have a 0 and the stack is empty, push it on the stack, and transition to q1
 - if you have a 1 and there is a 1 on the stack, push it on the stack, and transition to q1
 - if you have a 1 and there is a 0 on the stack, pop the 0 off, and transition to q1
 - if you have a 0 and there is a 0 or 1 on the stack, push it on the stack and stay in q0


I was wondering if this is allowed, and it knows what to do given the scenario?

Sorry if this is obvious, I have been looking at some PDAs and haven't seen any that have multiple options to transition between states and was wondering if it was allowed.
Simple answer: yes, that is allowed. In the example you give, it's simple--depending on the input symbol and the stack contents, there's one and only one choice for the action of the machine in state $q_0$. It's even possible to have several actions as consequence to a single (input, stack top) pair, like this,

-- input 0 and stack top 1, push 0 and go to state $q_2$

-- input 0 and stack top 1, push 1 and go to state $q_3$

Seems wierd, I know but such machines are called nondeterministic pushdown automata and are quite useful; look them up.