  Molecular spintronics hinges on the detailed understanding of electronic and
magnetic properties of molecules interfaced with various materials. Here we
demonstrate with ab-initio simulations that the prototypical Co-phthalocyanine
(CoPc) molecule can surprisingly develop multi-spin states once deposited on
the two-dimensional 2H-NbSe$_2$ layer. Conventional calculations based on
density functional theory (DFT) show the existence of low, regular and high
spin states, which reduce to regular and high spins states once correlations
are incorporated with a DFT+$U$ approach. Depending on $U$, the ground state is
either the low spin or high spin state with energy differences affected by the
molecular orientation on top of the substrate. Our results are compared to
recent scanning probe measurements and motivate further theoretical and
experimental studies on the unveiled rich multi-magnetic behavior of CoPc
molecule.
