Recently, \citeA{Biagioli2023} used a simple stochastic model to derive a dimensionless parameter to predict convective self aggregation (SA) development, which was based on the derivation of the maximum free convective distance ($d_{clr}$) expected in the pre-aggregated, random state. Our goal is to test and further investigate this hypothesis, namely that $d_{clr}$ can predict SA occurrence, using an ensemble of twenty-four distinct combinations of horizontal mixing, planetary boundary layer (PBL), and microphysical parameterizations. We conclude that the key impact of parameterization schemes on SA is through their control of the number of convective cores and their relative spacing, $d_{clr}$, which itself is impacted by cold-pool (CP) properties and mean updraft core size. SA is more likely when the convective core count is small, while CPs modify convective spacing via suppression in their interiors and triggering by gust-front convergence and collisions. Each parameterization scheme emphasizes a different mechanism. Subgrid-scale horizontal turbulent mixing mainly affects SA through the determination of convective core size and thus spacing. The sensitivity to the microphysics is mainly through rain evaporation and the subsequent impact on CPs, while perturbations to the ice cloud microphysics have a limited effect. Non-local PBL mixing schemes promote SA primarily by increasing convective inhibition through inversion entrainment and altering low cloud amounts, leading to fewer convective cores and larger $d_{clr}$.