For metal‐mediated host compounds, the development of strategies to reduce symmetry and introduce multiple functionalities in a non‐statistical way is a challenging task. We show that the introduction of steric stress around the coordination environment of square‐planar PdII cations and bis‐monodentate nitrogen donor ligands allows to control the size and shape of the assembled product, from [Pd2L4] cages over [Pd2L3] bowl‐shaped structures to [Pd2L2] rings. Therefore, banana‐shaped ligand backbones were equipped with pyridines, two different quinoline isomers and acridine, the latter three introducing steric congestion through hydrogen substituents on annelated benzene rings. Differing behavior of the four resulting hosts towards the binding of C60 and C70 fullerenes was studied and related to structural differences by NMR spectroscopy, mass spectrometry and single crystal X‐ray diffraction. The three cages based on pyridine, 6‐quinoline or 3‐quinoline donors were found to either bind C60, C70 or no fullerene at all.