First, we performed these calculations without any shift or regularization, which resulted in 117 states with a reference weight deviating by more than 10 % from the ground state one (109 for MS-CASPT2D). These were considered affected by intruder states, and hence excluded from the NOISP analysis. The MS-CASPT2 transition energies of the remaining 194 (202 for MS-CASPT2D) states form the set of reference values for the NOISP analysis, as they do not require any shift or regularization. The full set of 311 states are instead used in the ISP analysis. Please refer to Section 3.1 of the Supporting Information for the detailed account of which states are included in which analysis. In the NOISP analysis, we compare the results obtained with an increasing value of ε to the reference values (ε = 0). This provides a quantitative measure of the sensitivity of the excitation energies with respect to ε. Instead, in the ISP analysis we track the distribution of the reference weights as a function of ε. In particular, for each molecule we compute the relative deviation of the excited states proportion to the total number of states. Mathematically, this can be described as