Pd(II)-based low-symmetry coordination cages possessing anisotropic cavities are of great interest. The common strategies employed to achieve such cages utilize either more than one type of symmetrical ligands (e.g., Laa, Lbb, etc.) or only one type of unsymmetrical ligand (e.g., Lab). To significantly enhance the anisotropy, we have designed two unsymmetrical bidentate ligands i.e., Lab and Lcd, aiming a low-symmetry Pd2Lab2Lcd2-type cage. It was accomplished by high-fidelity integrative self-sorting of two different low-symmetry cages having Pd2Lab4 and Pd4Lcd8-type architectures (homoleptic complexes of the designed ligands). Structural constraints and geometry complementarity in the ligand design drive the non-statistical exclusive self-assembly of the Pd2Lab2Lcd2-type cage. By taking advantage of the complemental geometries between ligands, a low-symmetry Pd2Lab2Lcc2-type cage was also obtained. Heteromeric completive self-sorting of three homoleptic assemblies (Pd2Lab4, Pd4Lcc8 and Pd4Lcd8-type cages) into an exclusive mixture of Pd2Lab2Lcd2 and Pd2Lab2Lcc2-type mixed ligated assemblies was demonstrated through cage-to-cage transformations.