This paper presents a homogeneous system of magnetic colloidal particles that self-assembles via two structural patterns of different symmetry. Based on a qualitative comparison between a real magnetic particles system, analytical calculations and molecular dynamics simulations, it is shown that bistability can be achieved by a proper tailoring of an anisotropic magnetization distribution inside the particles. The presented bistability opens new possibilities to form two-dimensionally extended and flexible structures where the connectivity between the particles can be changed in vivo.