Modelling a dependency of multiple transitions on data in one place
I do not know if there is a variant of Petri nets that captures your intent exactly -- there probably is, there are so many -- but the feature can be expressed with regular Petri nets.

Just add a transition that creates tokens in multiple places, one per original transitions. Then, all three follow-up transitions can fire after the preceding one is done.



Introduce whatever syntax you want to express this neatly, and implement it using multiple places in the backend.