Steady-state flow and elastic behavior is investigated for the moderately concentrated binary suspensions of soft microgels (pastes) with chemically dissimilar surfaces, and various degrees of size- and stiffness disparities. The pastes of poly(N-isopropyl acrylamide) (N) and poly(N-isopropyl methacrylamide) (NM) microgels with different values of yield strain gamma(c)(gamma Nc >gamma NMc) are employed as the components. For the single microgel pastes (phi approximate to 1 where phi is apparent volume fraction), the values of gamma(c)are governed by the chemical species of constituent polymer in microgel surface whereas gamma(c)is insensitive to cross-link density and particle size. We demonstrate that the binary N/NM pastes with large size disparity (R-N/NM=D-N/D-NM< 0.26 whereDis the microgel diameter) at low phi(N)(phi(N): weight fraction of small N microgels) exhibit the peculiarities in several rheological aspects,i.e., the two-step yielding in steady-state flow, and their values of gamma(c)and equilibrium shear modulus (G(0)) being equivalent to those of the single large NM microgel paste. These peculiarities are attributed to the characteristic packing resulting from large size disparity in which all or almost of the small N microgels tend to be accommodated in the gap between the large NM microgels even in moderately concentrated state. This characteristic packing substantially masks the contribution of the small N microgels at low phi(N), explaining the phi(N)-independentG(0)and gamma(c)as well as the first yielding governed solely by the large NM microgels. The second yielding results from the emerged contribution of the small N microgels expelled out from the gap by the positional rearrangements after the first yielding. The binary homo-N/N pastes with the similarly large size disparity at low phi(small)also exhibit the phi(small)-independent values ofG(0), but they show one-step yielding, indicating that the two-step yielding requires not only sufficiently large size disparity but also chemical dissimilarity (different values of gamma(c)) between the two components.