Clouds play crucial roles in regulating energy and hydrological cycle in the climate system. However, representing cloud processes in global climate models (GCMs) is one of the most challenging problems because of the multi-scale nature of these processes. The multi-scale modeling framework (MMF), also known as super-parameterization that embeds a cloud-resolving model within each GCM grid column, provides a promising tool for addressing this challenge. Here, we develop an MMF with the Predicted Particle Properties (P3) scheme that has an advanced ice microphysics parameterization. In this scheme, ice properties are predicted and they can evolve more naturally in time and space based on the relative degree of riming and vapor deposition in their growth. This is in contrast to the Morrison microphysics originally used in the MMF, which artificially separates ice into several predefined categories. We will present the cloud and precipitation simulation in this new MMF. We compare the MMF simulations with P3 and with Morrison microphysics against available observations, in particular focusing on the variability of cloud properties and precipitation. We find that, compared to the simulation with Morrison microphysics, the simulation with the P3 microphysics overall predicts more frequent moderate and heavy precipitation rates, more realistic convective updrafts, and radar reflectivity as in the observations over the Central United States during the Midlatitude Continental Convective clouds Experiment in 2011.