  Recent studies have shown that the local mass-metallicity (M-Z) relation
depends on the specific star formation rate (SSFR). Whether such a dependence
exists at higher redshifts, and whether the resulting M-Z-SFR relation is
redshift invariant, is debated. We re-examine these issues by applying the
non-parametric techniques of Salim et al. (2014) to ~130 $z\sim2.3$ galaxies
with N2 and O3 measurements from KBSS (Steidel et al. 2014). We find that the
KBSS M-Z relation depends on SSFR at intermediate masses, where such dependence
exists locally. KBSS and SDSS galaxies of the same mass and SSFR ("local
analogs") are similarly offset in the BPT diagram relative to the bulk of local
star-forming galaxies, and thus we posit that metallicities can be compared
self-consistently at different redshifts as long as the masses and SSFRs of the
galaxies are similar. We find that the M-Z-SFR relation of $z\sim2$ galaxies is
consistent with the local one at $\log M_*<10$, but is offset up to -0.25 dex
at higher masses, so it is altogether not redshift invariant. This high-mass
offset could arise from a bias that high-redshift spectroscopic surveys have
against high-metallicity galaxies, but additional evidence disfavors this
possibility. We identify three causes for the reported discrepancy between N2
and O3N2 metallicities at $z\sim2$: (1) a smaller offset that is also present
for SDSS galaxies, which we remove with new N2 calibration, (2) a genuine
offset due to differing ISM condition, which is also present in local analogs,
(3) an additional offset due to unrecognized AGN contamination.
