We extend the SG4 generalized gradient approximation, developed for covalent and ionic solids with a nonlocal van der Waals functional. The resulting SG4-rVV10m functional is tested, considering two possible parameterizations, for various kinds of bulk solids including layered materials and molecular crystals as well as regular bulk materials. The results are compared to those of similar methods, PBE + rVV10L and rVV10. In most cases, SG4-rVV10m yields a quite good description of systems (from iono-covalent to hydrogen-bond and dispersion interactions), being competitive with PBE + rVV10L and rVV10 for dispersion-dominated systems and slightly superior for iono-covalent ones. Thus, it shows a promising applicability for solid-state applications. In a few cases, however, overbinding is observed. This is analysed in terms of gradient contributions to the functional.