  Precision searches for time-reversal symmetry violating interactions in polar
molecules are extremely sensitive probes of high energy physics beyond the
Standard Model. To extend the reach of these probes into the PeV regime, long
coherence times and large count rates are necessary. Recent advances in laser
cooling of polar molecules offer one important tool -- optical trapping.
However, the types of molecules that have been laser-cooled so far do not have
the highly desirable combination of features for new physics searches, such as
the ability to fully polarize and the existence of internal co-magnetometer
states. We show that by utilizing the internal degrees of freedom present only
in molecules with at least three atoms, these features can be attained
simultaneously with molecules that have simple structure and are amenable to
laser cooling and trapping.
