Part of Summoner's thing in FFXI was doing solo summon challenges in order to summon them. FFXIV keeps that spirit in its job quests by having you do a solo duty against a primal, but we only ever get the 3 original primals from the early game. There's also the egi-glamour system we were promised that seemingly got sidelined after Carbuncle.

What if they combined the egi-glamour system with solo SMN duties? There have been a lot of primals so far that could be turned into SMN-only duties, and when you clear you gain the egi-glamour. If you already have the clear, make them replayable for tomes. Have a summoner spellbook menu where you pick which glamour goes on each pet type, with each primal being locked to a single type that fits it. Each patch could add a few more to go get.

Attack type: Ifrit, Leviathan, Ravana, Zurvan, Odin, Susano
Tank type: Titan, Bismarck, Sephirot, King Mog
Caster Type: Garuda, Shiva, Ramuh, Sophia, maybe Lakshmi?

Byakko, Suzaku and Seiryu may not fit thematically as they're not primals but it'd be cool to see them as well. Phoenix or Tsukuyomi would be nice too.

The skills for each could have the same effects per pet type for balance reasons, maybe with different names/animations if they want to go that far (because Leviathan using Flaming Crush would be a bit odd).