  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
