In this paper, we develop a non-reductive variant of the regularity theory of causation proposed in Andreas and Günther (Pacific Philosophical Quarterly 105: 2–32, 2024). The variant is motivated as a refinement of Lewis’s (Journal of Philosophy 70:556–567, 1973) regularity theory. We do not pursue a reductive theory here because we found a challenge for Baumgartner's (Erkenntnis 78:85–109, 2013) regularity theory which applies to our previous theory as well. The challenge is sidestepped by a framework of law-like propositions resembling structural (...) equations. We furthermore improve the deviancy condition of our previous theory. Finally, we show that the present theory can compete with the most advanced regularity and counterfactual accounts. (shrink)