We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids
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