In this manuscript we investigate the shear rheology, sedimentation stability and redispersibility characteristics of bimodal MR fluids with a large-to-small size ratio sigma(L)/sigma(s) approximate to 100 where the small-size population of particles is in the single-multidomain limit (sigma(s) approximate to 100 nm) to promote the formation of core-shell supraparticles (i.e., large particles surrounded by the smaller ones). We focus on the effect of mixing the two kinds of particles in different proportions while keeping either the large particle volume fraction or the total volume fraction constant. Five different nanoparticles, having different chemical compositions and shapes, are investigated in this work: barium ferrite, magnetite, iron, chromium dioxide, and goethite. The results demonstrate that nanoparticles fill the voids between microparticles, and this locally enhances the magnetic field. The on-state yield stress and effective enhancement may increase or decrease depending on the magnetization of the nanoparticles as compared to that of the microparticles. An enhanced MR effect is experimentally observed and also simulated with finite element methods, when the magnetization of the nanoparticles is larger than that of the microparticles. Bimodal MR fluids exhibit better penetration and redispersibility response than the monomodal counterparts and dimorphic magnetorheological fluids based on nanofibers.