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Existing star-forming vs. active galactic nucleus (AGN) classification schemes using optical emission-line diagnostics mostly fail for low-metallicity and/or highly star-forming galaxies, missing AGN in typicalz∼ 0 dwarfs. To recover AGN in dwarfs with strong emission lines (SELs), we present a classification scheme optimizing the use of existing optical diagnostics. We use Sloan Digital Sky Survey emission-line catalogs overlapping the volume- and mass-limited REsolved Spectroscopy Of a Local VolumE (RESOLVE) and Environmental COntex (ECO) surveys to determine the AGN percentage in SEL dwarfs. Our photoionization grids show that the [Oiii]/Hβversus [Sii]/Hαdiagram (Siiplot) and [Oiii]/Hβversus [Oi]/Hαdiagram (Oiplot) are less metallicity sensitive and more successful in identifying dwarf AGN than the popular [Oiii]/Hβversus [Nii]/Hαdiagnostic (Niiplot or “BPT diagram”). We identify a new category of “star-forming AGN” (SF-AGN) classified as star-forming by the Niiplot but as AGN by the Siiand/or Oiplots. Including SF-AGN, we find thez∼ 0 AGN percentage in dwarfs with SELs to be ∼3%–16%, far exceeding most previous optical estimates (∼1%). The large range in our dwarf AGN percentage reflects differences in spectral fitting methodologies between catalogs. The highly complete nature of RESOLVE and ECO allows us to normalize strong emission-line galaxy statistics to the full galaxy population, reducing the dwarf AGN percentage to ∼0.6%–3.0%. The newly identified SF-AGN are mostly gas-rich dwarfs with halo mass <10^11.5M_⊙, where highly efficient cosmic gas accretion is expected. Almost all SF-AGN also have low metallicities (Z≲ 0.4Z_⊙), demonstrating the advantage of our method.