Personally I am of the opinion of changing egis to function as the Demi-primals rather then being a constant pet. Just make it so that in the higher levels the Egis upgrade completely into Demis visually. Basically treating the egi form as being the strongest form we could draw at the time, but they get upgraded to full demis later as we have gotten stronger and can unleash a stronger version of them.

This could also allow for other primals to be brought in. You could have a demi rotation of Ifrit>Garuda>Titan>Bahamut>Levi>Ramuh>Shiva>Phoenix. Thus you are constantly summoning primals to perform big moves like in other FF games. Other options for more primal summons also include being able to make some of the longer cooldown skills be one time summons or change some skills into cooldown ones that are applied via the summon. To use an example remove Physick and in its place put in a 60-120 sec cooldown ability that Summons Demi-Lakshmi to heal the party.