The Quasi-3-D Multiscale Modeling Framework (Q3D MMF) is a second-generation MMF, which has following advances over the first-generation MMF: 1) The cloud-resolving models (CRMs) that replace conventional parameterizations are not confined to the large-scale dynamical-core grid cells, and are seamlessly connected to each other, 2) The CRMs sense the three-dimensional large- and cloud-scale environment, 3) Two perpendicular sets of CRM channels are used, and 4) The CRMs can resolve the steep surface topography along the channel direction. The basic design of the Q3D MMF has been developed and successfully tested in a limited-area modeling framework. Currently, global versions of the Q3D MMF are being developed for both weather and climate applications. The dynamical cores governing the large-scale circulation in the global Q3D MMF are selected from two cube-based global atmospheric models. The CRM used in the model is the 3-D nonhydrostatic anelastic Vector-Vorticity Model (VVM), which has been tested with the limited-area version for its suitability for this framework. As a first step of the development, the VVM has been reconstructed on the cubed-sphere grid so that it can be applied to global channel domains and also easily fitted to the large-scale dynamical cores. We have successfully tested the new VVM by advecting a bell-shaped passive tracer and simulating the evolutions of waves resulted from idealized barotropic and baroclinic instabilities. For improvement of the model, we also modified the tracer advection scheme to yield positive-definite results and plan to implement a new physics package that includes a double-moment microphysics and an aerosol physics. The interface for coupling the large-scale dynamical core and the VVM is under development. In this presentation, we shall describe the recent progress in the development and show some test results.