Stellar population models produce radiation fields that ionize oxygen up to O +2 , defining the limit of standard H II region models (< 54.9 eV). Yet, some extreme emission line galaxies, or EELGs, have surprisingly strong emission originating from much higher ionization potentials. We present UV-HST/COS and optical-LBT/MODS spectra of two nearby EELGs that have very-high-ionization emission lines (e.g., He IIλλ1640,4686 C IVλλ1548,1550, [Fe V]λ4227, [Ar IV]λλ4711,4740). We define a 4-zone ionization model that is augmented by a very-high-ionization zone, as characterized by He +2 (> 54.4 eV).The 4-zone model has little to no effect on the measured total nebular abundances, but does change the interpretation of other EELG properties: we measure steeper central ionization gradients, higher volume-averaged ionization parameters, and higher central T e , n e , and logU values. Traditional 3-zone estimates of the ionization parameter can under-estimate the average logU by up to 0.5 dex. Additionally, we find a model-independent dichotomy in the abundance patterns, where the α/H-abundances are consistent but N/H, C/H, and Fe/H are relatively deficient, suggesting these EELGs are α/Fe-enriched by > 3×. However, there still is a high-energy ionizing photon production problem (HEIP 3 ). Even for such α/Fe-enrichment and very-high logUs, photoionization models cannot reproduce the very-high-ionization emission lines observed in EELGs.