The Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS) is a bulk microphysics framework that calculates process rates using generalized power laws of the moments of the droplet size distribution. Formula parameters are inferred with Monte Carlo methods, evaluating a proposed set of parameter values by comparing model outputs to observations. In this study, we produce a set of 2- and 3-moment BOSS schemes that effectively emulate the behavior of a bin microphysics model, using an idealized 1D driver for various forcing conditions that produce either non-precipitating or drizzling cloud. In this driver, BOSS is fully responsible for collision-coalescence, condensation/evaporation, and calculation of hydrometeor fall speeds, with only dynamical forcing and droplet activation handled externally. Comparing BOSS schemes with different terms and different numbers of prognostic cloud moments allows us to evaluate whether the model benefits from the added complexity of these changes. BOSS also has an advantage over black-box machine-learning methods in that the process rate formulas are “human-readable”, allowing us to analytically identify potential sources of instability.