Ionization sources other than HII regions give rise to the right-hand branch in the standard ([NII]) BPT diagram, populated by Seyfert 2s and LINERs. However, because the majority of Seyfert/LINER hosts are star forming (SF), HII regions contaminate the observed lines to some extent, making it unclear if the position along the branch is merely due to various degrees of mixing between pure Seyfert/LINER and SF, or whether it reflects the intrinsic diversity of Seyfert/LINER ionizing sources. In this study, we empirically remove SF contributions in ∼100,000 Seyfert/LINERs from SDSS using the doppelganger method. We find that mixing is not the principal cause of the extended morphology of the observed branch. Rather, Seyferts/LINERs intrinsically have a wide range of line ratios. Variations in ionization parameter and metallicity can account for much of the diversity of Seyfert/LINER line ratios, but the hardness of ionization field also varies significantly. Furthermore, our k-means classification on seven decontaminated emission lines reveals that LINERs are made up of two populations, which we call soft and hard LINERs. The Seyfert 2s differ from both types of LINERs primarily by higher ionization parameter, whereas the two LINER types mainly differ from each other (and from starforming regions) in the hardness of the radiation field. We confirm that the [NII] BPT diagram more efficiently identifies LINERs than [SII] and [OI] diagnostics, because in the latter many LINERs, especially soft ones, occupy the same location as pure star-formers, even after the SF has been removed from LINER emission.