Here I will list potential compatibility and non-compatibilities. You are welcome to experiment with your favorite mods to see how well they jive with the TPE. I will also explore compatibilities, and am open to suggestions.

Initial Compat List:
Compatible:
Ancient Cache of Technologies et al
Astronomical Emblem Pack
Cybrxkhan's Assortment of Namelists
Extra Ship Components
Fantastical Magiks
Flags: Emblems & Backgrounds
Gigastructures and More
Guilli's Planet Modifiers
Guilli's Technologies
Hemo's Dynamic Difficulty
More Events Mod
Product Placement emblem Pack
Real Space et al
Real Habitability
Zenith of Fallen Empires et al

Unsure:

Non-Compatible:
Stellaris Immortal (Since this mod is incompatible, I will scrounge the workshop and build performance boosters into this mod, or otherwise recommend them when I can, to try to reduce late game lag.)
Stellaris Reborn
Any mod that conflicts with Real Space, Elves of Stellaris, or Arcane Heritage.
Any mod that adds stars to the galactic core.
Dynamic Political Events (Certain elements of DPE refuses to obey TPE canon, no matter what I did to try to override DPE ;_; )