I have taught the Beavers model of family systems in my family life class for many years.
Recently I have been immersed in "critical realist" social theory. One of the most attractive features of critical realism is the idea that real things - things with the power to cause other effects - are not simply real or not-real, but can emerge into reality.
I see a way to combine the two.
The Beavers sequence of family systems is, from least functional to most functional, Chaos, Tyranny, Rule-Bound, Adequate, and Optimal.
As these systems affect the emergence of a family into fully functional reality, the sequence could be:
Chaos - prevents the emergence of a higher-order functioning system.
Tyranny - achieves minimal order, but can only be defensive; it is a necessary precondition for emergence, but is not sufficient.
Rule-Bound - is a minimally emergent reality. The system exists independent of its elements (the individual family members).
Adequate - is an emergent reality with creativity
Optimal - is an emergent reality with creativity and resilience.