  Current methods of identifying the ionizing source of nebular emission in
galaxies are well defined for the era of single fiber spectroscopy, but still
struggle to differentiate the complex and overlapping ionization sources in
some galaxies. With the advent of integral field spectroscopy, the limits of
these previous classification schemes are more apparent. We propose a new
method for distinguishing the ionizing source in resolved galaxy spectra by use
of a multi-dimensional diagnostic diagram that compares emission line ratios
with velocity dispersion on a spaxel by spaxel basis within a galaxy. This new
method is tested using the SAMI Galaxy Survey Data Release 3, which contains
3068 galaxies at z $<$ 0.12. Our results are released as ionization maps
available alongside the SAMI DR3 public data. Our method accounts for a more
diverse range of ionization sources than the standard suite of emission line
diagnostics; we find 1433 galaxies with significant contribution from
non-star-forming ionization using our improved method as compared to 316
galaxies identified using only emission line ratio diagnostics. Within these
galaxies, we further identify 886 galaxies hosting unique signatures
inconsistent with standard ionization by H2 regions, AGN, or shocks. These
galaxies span a wide range of masses and morphological types and comprise a
sizable portion of the galaxies used in our sample. With our revised method, we
show that emission line diagnostics alone do not adequately differentiate the
multiple ways to ionize gas within a galaxy.
