This study presents the role of 5d orbitals in the bonding, and electronic and magnetic structure of Ce imido and oxo complexes synthesized with a tris(hydroxylaminato) [((2-^tBuNO)C₆H₄CH₂)₃N]³⁻ (TriNO_x³⁻) ligand framework, including the reported synthesis and characterization of two new alkali metal-capped Ce oxo species. X-ray spectroscopy measurements reveal that the imido and oxo materials exhibit an intermediate valent ground state of the Ce, displaying hallmark features in the Ce L_III absorption of partial f-orbital occupancy that are relatively constant for all measured compounds. These spectra feature a double peak consistent with other formal Ce(IV) compounds. Magnetic susceptibility measurements reveal enhanced levels of temperature-independent paramagnetism (TIP). In contrast to systems with direct bonding to an aromatic ligand, no clear correlation between the level of TIP and f-orbital occupancy is observed. CASSCF calculations defy a conventional van Vleck explanation of the TIP, indicating a single-reference ground state with no low-lying triplet excited state, despite accurately predicting the measured values of f-orbital occupancy. The calculations do, however, predict strong 4f/5d hybridization. In fact, within these complexes, despite having similar f-orbital occupancies and therefore levels of 4f/5d hybridization, the d-state distributions vary depending on the bonding motif (CeO vs. CeN) of the complex, and can also be fine-tuned based on varying alkali metal cation capping species. This system therefore provides a platform for understanding the characteristic nature of Ce multiple bonds and potential impact that the associated d-state distribution may have on resulting reactivity.