  Correlations between intrinsic galaxy shapes on large-scales arise due to the
effect of the tidal field of the large-scale structure. Anisotropic primordial
non-Gaussianity induces a distinct scale-dependent imprint in these tidal
alignments on large scales. Motivated by the observational finding that the
alignment strength of luminous red galaxies depends on how galaxy shapes are
measured, we study the use of two different shape estimators as a multi-tracer
probe of intrinsic alignments. We show, by means of a Fisher analysis, that
this technique promises a significant improvement on anisotropic
non-Gaussianity constraints over a single-tracer method. For future weak
lensing surveys, the uncertainty in the anisotropic non-Gaussianity parameter,
$A_2$, is forecast to be $\sigma(A_2)\approx 50$, $\sim 40\%$ smaller than
currently available constraints from the bispectrum of the Cosmic Microwave
Background. This corresponds to an improvement of a factor of $4-5$ over the
uncertainty from a single-tracer analysis.
