Biomass burning plumes are frequently transported over the southeast Atlantic (SEA) stratocumulus deck during the southern African fire season (June-October). The plumes bring large amounts of absorbing aerosols and enhanced moisture, which can trigger a rich set of aerosol-cloud-radiation interactions with climatic consequences that are still poorly understood. We use large-eddy simulation (LES) to explore and disentangle the individual impacts of aerosols and moisture on the underlying stratocumulus clouds, the marine boundary layer (MBL) evolution, and the stratocumulus-to-cumulus transition (SCT) for three different meteorological situations over the southeast Atlantic during August 2017. For all three cases, our LES shows that the SCT is driven by increased sea surface temperatures and cloud-top entrainment as the air is advected towards the Equator. In the LES model, aerosol indirect effects, including impacts on drizzle production, have a small influence on the modeled cloud evolution and SCT, even when aerosol concentrations are lowered to background concentrations. In contrast, local semi-direct effects, i.e., aerosol absorption of solar radiation in the MBL, cause a reduction in cloud cover that can lead to a speed-up of the SCT, in particular during the daytime and during broken cloud conditions, especially in highly polluted situations. The largest impact on the radiative budget comes from aerosol impacts on cloud albedo: the plume with absorbing aerosols produces a total average 3 d of simulations. We find that the moisture accompanying the aerosol plume produces an additional cooling effect that is about as large as the total aerosol radiative effect. Overall, there is still a large uncertainty associated with the radiative and cloud evolution effects of biomass burning aerosols. A comparison between different models in a common framework, combined with constraints from in situ observations, could help to reduce the uncertainty.