We review the class of partial-propensity exact stochastic simulation algorithms (SSA) for chemical reaction networks. We show which modules partial-propensity SSAs are composed of and how partial-propensity variants of known SSAs can be constructed by adjusting the sampling strategy used. We demonstrate this on the example of two instances, namely the partial-propensity variant of Gillespie's original direct method and that of the SSA with composition-rejection sampling (SSA-CR). Partial-propensity methods may outperform the corresponding classical SSA, particularly on strongly coupled reaction networks. Changing the different modules of partial-propensity SSAs provides flexibility in tuning them to perform particularly well on certain classes of reaction networks. The framework presented here defines the design space of such adaptations.