I suppose it's possible. Wasn't said that pieces of a primals original being is spread throughout the Lifestream?

I'd say as long as the interpretation of __ primal is different, then it's possible to summon 2 of the same Primals ... kinda like FF 10's Aeons.

Ex: One version of Garuda is a sadistic fighter due to drinking the blood of the Serpent Lord, while the other Ixal can interpret her as a noble freedom fighter.

In the end, it's the belief of the follower's that shape the personality (maybe even appearance) of the summoned Primal. Afterall, Ysayle/heretic's Shiva is not a robed and calm woman.

To a lesser extent, Egis can still exist despite the Primal being around.

Though Anonymoose does have a good point: Once a Primal is captured (Dalamud, Ultima, Great Seal at the Lake) their essence is trapped, thus can no longer be summoned.