Lore: Discover an Allagan device that transfers the Primal's Aether to a storage device.
Edit: Well lore wise the Allagan have been dealing with and manipulating the primals; Summoner Egis, Ultima Weapon, and even Dalamud come to mind. It's not to far fetch for them to build a device to capture a primals aether and create a unstable clone of the primal to do their bidding.
Edit: There needs to be something that happens that allows primals to willfully manifest themselves into existence without the use of crystals. Then again it's know that primals existence during Allagan Empire and the third age. It's also know that it wasn't the beastmen that summoned them during that time because it was the Ascian that taught them how in 1.xx. It could be the natural state of primals was to roam free and only when the seal was created over Silvertear Falls that this process was corrupted.
Concept would first involve adding roaming primals to the open world. Base it on the FATE system that announces spawn on map and hp based on amount of player from previous fight. Be sure to have all the mechanics from Trials to make it fun and entertaining.
Next it the summoning system. Every time a FC member defeats the roaming primal they build up the Allagan's Device gauge. Once full they can release the primal against an enemy and then it fades back to the Aether.
Now for the primals themselves. To add damage that would equal a second Limit Break could be over powered. Players do want flashy summons that not only do damage but also do some kind of support ability. The compromise would be a summon that does damage and buff/debuffs.
Key Points:
-Roaming Primals
-FC Summoning Gauge
-Primals that add damage and buff/debuff.