Stellar population models produce radiation fields that ionize oxygen up to O+2, defining the limit of standard HII 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., HeII 1640,4686 CIV 1548,1550, [FeV] 4227, [ArIV] 4711,4740). 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 log U by up to 0.5 dex. Additionally, we find a model-independent dichotomy in the abundance patterns, where the alpha/H-abundances are consistent but N/H, C/H, and Fe/H are relatively deficient, suggesting these EELGs are alpha/Fe-enriched by >3 times. However, there still is a high-energy ionizing photon production problem (HEIP^3). Even for such alpha/Fe-enrichment and very-high log Us, photoionization models cannot reproduce the very-high-ionization emission lines observed in EELGs.
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