Cool idea! Effectively you're defining a generalization of the notion of a critical pair or branch pair to a "critical tuple" or "branch tuple". Of course, as I outline in my papers (https://www.wolframphysics.org/technical-documents/), there is quite a bit of subtlety involved when converting between ideas involving confluence (i.e. convergence of branch pairs) to ideas involving causal invariance (i.e. all branches of multiway evolution yielding causal networks that are isomorphic as directed acyclic graphs). Confluence is a necessary, but not sufficient, condition for causal invariance in the usual case.

I can't immediately see what the connection between, say, 3-2-confluence and the combinatorial structure of the resultant causal graphs would be (presumably some weakened form of an isomorphism condition, but precisely which kind of weakening is far from clear); this would be a really cool project for someone to investigate! I heartily encourage people to try to figure this out, and let me know what they find :)