Nature provides examples of self-assemble lightweight disordered network structures with remarkable mechanical properties which are desirable for many application purposes but challenging to reproduce artificially. Previous experimental and computational studies investigated the mechanical responses of random network structures focusing on topological and geometrical aspects in terms of variable connectivity or probability to place beam elements. However, for practical purposes, an ambitious challenge is to design new materials with the possibility to tailor their mechanical features such as stiffness. Here, we design a two dimensional disordered mechanical meta-material exhibiting unconventional stiffness-density scaling in the regime where both bending and stretching are relevant for deformation. In this regime, the mechanical meta-material covers a wide interval of the Young modulus-density plane, simultaneously exhibiting high critical stress and critical strain. Our results, supported by finite element simulations, provide the guiding principles to design on demand disordered metamaterials, bridging the gap between artificial and naturally occurring materials.