Four BINOL-based bis(4-pyridyl) ligands were synthesised in enantiopure and racemic form. These ligands form metallosupramolecular [(dppp)2M2L2] rhombi with cis-protected [(dppp)Pd]2+ and [(dppp)Pt]2+ ions. In principle, racemic ligands can self-assemble into three stereoisomeric rhombi. The degree of self-sorting in the self-assembly process crucially depends on the substitution pattern and the resulting bend angle of the V-shaped ligands as well as the degree of steric crowding within the assembly when racemic ligands are used. Thus, these processes either lead to homochiral assemblies in a narcissistic self-recognition manner, to heterochiral assemblies in a social self-discriminating manner, or proceed in a nonselective fashion as evidenced by NMR spectroscopy, mass spectrometry and single-crystal X-ray diffraction.