In the original multiscale modeling framework (MMF), the Community Atmosphere Model (CAM3.5) is used as the host general circulation model (GCM), and the System for Atmospheric Modeling model with a first-order turbulence closure is used as the cloud resolving model (CRM) for representing cloud physical processes in each grid column of the GCM. This study introduces an upgrade of the MMF in which the first-order turbulence closure scheme is replaced by an advanced third-order turbulence closure in its CRM component. The results are compared between the upgraded and original MMFs, CAM3.5, and observations. The global distributions of low-level cloud amounts in the subtropics in the upgraded MMF show substantial improvement relative to the original MMF when both are compared with observations. The improved simulation of low-level clouds is attributed not only to the representation of subgrid-scale condensation in the embedded CRM but also is closely related to the increased surface sensible and latent heat fluxes, the increased lower tropospheric stability (LTS), and stronger longwave radiative cooling. Both MMF simulations show close agreement in the vertical structures of cloud amount and liquid water content of midlatitude storm-track clouds and subtropical low-level clouds, compared with observations, with the upgraded MMF being better at simulating the low-level cumulus regime. Since the upgraded MMF produces more subtropical low-level clouds and does not produce an excessive amount of optically thick high-level clouds in either the tropics or midlatitudes as the original MMF does, the global mean albedo decreases. The positive bias in albedo and longwave cloud radiative forcing (CRF) and negative bias in shortwave CRF are reduced in the tropical convective regions.