The reaction counts chemical master equation (CME) is a high-dimensional variant ofthe classical population counts CME. In the reaction counts CME setting, we count the reactionswhich have fired over time rather than monitoring the population state over time. Since a reactioneither fires or not, the reaction counts CME transitions are only forward stepping. Typically thereare more reactions in a system than species, this results in the reaction counts CME being higher indimension, but simpler in dynamics. In this work, we revisit the reaction counts CME frameworkand its key theoretical results. Then we will extend the theory by exploiting the reactions counts’forward stepping feature, by decomposing the state space into independent continuous-time Markovchains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimatesfor the CTMC decomposition of the CME. This new theory gives new insights into solving hittingtimes-, rare events-, and a priori domain construction problems.