A broad class of reaction networks are controlled not by any thermodynamic ensemble but by rates and are referred to as "kinetically constrained". Here, microkinetic rate theory is extended into a model of arbitrarily complex reaction networks. This microkinetic rate theory takes a form where the constraints imposed by kinetically constrained systems apply naturally. This model is compared to numerically complete results and is shown to be quantitatively predictive. Model deviations are shown to emerge for systems with incomplete mixing. This model is analytical and may serve as a basis for device and continuum scale rate modeling.