In this work, the yield stress previously measured for some ferrofluid-based magnetorheological fluids (FF-MRFs) with various volume fractions of nanosize magnetite (phi) and micrometer size iron particle (Phi(Fe)), for a wide range of magnetic fields (B), is further investigated from a new point of view. The mean magnetization (MM) approximation developed for conventional magnetorheological (MR) suspensions is extended to FF-MRFs and a characteristic magnetic stress is defined and determined by using the average iron particles magnetization in FF-MRF suspensions. We thus generate a rheological master curve of static yield stress vs characteristic magnetic stress, for different values of phi, Phi(Fe), and B by using a single variable, the characteristic magnetic stress, which contains only data that can be determined experimentally. This indicates, for the first time in literature, a concentration-magnetization superposition in the case of FF-MRFs. This master curve is useful to determine an optimal composition that allows one to obtain FF-MRFs with the best possible MR properties for a particular application. We also find that, regardless of the magnetite nanoparticles' volume fraction in the carrier ferrofluid, when the iron volume fraction is close to Phi(Fe)* = 30% a change in magnetorheological behavior appears; this is most probably due to the structural transition from chainlike structures of iron particles to more complex ones. In addition, in order to show that the MM approximation may be used even for the FF-MRFs, we employ the finite element method (FEM) to compute a characteristic force and a characteristic magnetic stress by considering a very simple model of a FF-MRF. We find that the FEM model developed for FF-MRFs on the basis of the MM approximation gives reasonably good results especially for low and saturation magnetic field regimes. (C) 2018 The Society of Rheology.