What about Structural Equation Modeling?

SEM under the Multi-Evidence Paradigm is distinct from Pearl’s Structural Causal Model and is not to be thought of as a counterfactual method. Rather, it is a method for evaluating causal network hypotheses against data repeatedly. It fits under the Multi-Evidence Paradigm as its use requires existing causal knowledge. 

Points to be Aware of:

SEM, in its historical form, is a methodology that adheres to a Hypothetico-Deductive philosophy (more precisely an Abductive science philosophy that strives over time to approach the best explanation using all available evidence). It is expected that initial scientific knowledge will be used to craft an informed initial path model supported by mechanistic knowledge and efforts to avoid confounding based on known confounders. The expectations from that model are compared to data observations as evaluations of the initial hypotheses. SEM studies are expected to pass through “model building”, “model comparing”, and “model confirming” stages as result of sustained application of SEM methods focused on external consistency. Chapter 10 in the book Structural Equation Modeling and Natural Systems (2006) entitled “The Systematic Use of SEM” describes the philosophy. 

In 2016, an illustration of what this knowledge-building approach can achieve was demonstrated in "Integrative modelling reveals mechanisms linking productivity and plant species richness." Nature 529.7586: 390-393.