I'd like to present the users with 3 buttons on the Start Advanced Workflow wizard that would kick off different transitions depending on what's clicked…
If not that, then I'd like to be able to kick off different transitions based on document aspect values.
The Start Advanced Workflow wizard is not sensitive to multiple transitions on the 'start' node.
However, you can use a decision node to select transitions. A decision node can use javascript to evaluate which transition to take. So, you can interrogate aspects, properties etc during the evaluation.