Trey added the Way Huge Supa-Puss to the rig in Summer 2015, presumably to replace the Fulltone Tape Delay that he had been tweaking to great effect on previous tours. The Supa-Puss was designed by pedal mastermind Jeorge Tripps, founder of Way Huge, the boutique pedal builder that was eventually absorbed by effects behemoth Dunlop.
The Supa-Puss, like the Moog 104M that replaced it, is a tap-tempo, bucket brigade-based analog delay (BBD) pedal, featuring 6 analog delay chips for a total of 900ms of delay time (though you can “trick” the pedal into giving you 3 seconds of delay by using the tap tempo).
This pedal enjoyed a spot in the main effects signal chain and atop the effects rack from 2015 until it was replaced by the 104M in Summer 2017. But at the same time, Trey switched from his old Languedoc Cabinets to the Komet Ambikabs, and the Supa-Puss was moved to the effects loop of the Ambikab beside the Eventide Space Echo. In this position, the Supa-Puss is used for more subtle delays while the 104M is used for bigger, bolder, more noticeable sounds.

Later, the 104m was removed and Trey went back to having the Supa Puss delays in front of the Ambikabs. The Ambikab delays were replaced with Eventide Space Reverbs and then customized Keeley Eccos delay/reverbs.
For a time, around summer 2019, Trey used 3 of these pedals in his signal chain, all controlled by the RST-24. One was called “ECHO” and was used as an almost-always-on very mild delay. The other 2 were called “SUPA” and “PUSS”. SUPA, pictured above, has the tap tempo set to the dotted eighth setting, while PUSS is set to the quarter note setting. The latter two remain in the rig today.