Fe(II)-porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)-porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex's highly correlated electronic structure. This technique is used to parse the numerous interactions of two low-lying triplet states (3A2g and 3Eg) and to show that strong metal d-d and macrocycle π-π orbital interactions preferentially stabilize the 3A2g state. d-π interactions, on the other hand, preferentially stabilize the 3Eg state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)-porphyrin model's full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.