One of the key challenges of metallo‐supramolecular chemistry is to maintain the ease of self‐assembly but, at the same time, create structures of increasingly high levels of complexity. In palladium(II) quadruply stranded lantern‐shaped cages, this has been achieved through either 1) the formation of heteroleptic (multi‐ligand) assemblies, or 2) homoleptic assemblies from low‐symmetry ligands. Heteroleptic cages formed from low‐symmetry ligands, a hybid of these two approaches, would add an additional rich level of complexity but no examples of these have been reported. Here we use a system of ancillary complementary ligand pairings at the termini of cage ligands to target heteroleptic assemblies: these complementary pairs can only interact (through coordination to a single Pd(II) metal ion) between ligands in a cis position on the cage. Complementarity between each pair (and orthogonality to other pairs) is controlled by denticity (tridentate to monodentate or bidentate to bidentate) and/or hydrogen‐bonding capability (AA to DD or AD to DA). This allows positional and orientational control over ligands with different ancillary sites. By using this approach, we have successfully used low‐symmetry ligands to synthesise complex heteroleptic cages, including an example with four different low‐symmetry ligands.