So I've known about this for a year, even demonstrated to a GM in person. If you use Sic/Ready just before your pets initial auto-attack after using fight, it will use two TP moves at the same time, at the cost of one Sic/Ready charge and 100% TP. Jug pets can and will often use TP moves they aren't able to use otherwise.
Is this common knowledge? I've done it quite a few times on accident, but was flipping through screenshots and saw I had taken one of Nazuna using two Lamb Chops at the same time opposed to auto-attacking. The first time I notice this happening was charming the Kraken in Qufim for extremely fast EXP through FoV pages at level ~24-30 (Familiar).
Here's the shot I took:
As well as a picture I'd found on the wiki:
The second photo displays Fargann using a TP move it does not even have access to, Sand Breath. I've reported this twice to GMs as a bug report, but it hasn't been fixed. Bored so I felt like sharing after seeing my old screenshot. :X