Simply put: no?

While theoretically it should be possible to summon multiple copies of the same primal, remember that they are all born from the same faith. As long as it's the same god (or phantom god) people are praying to, it will simply boost the power of the already-summoned Primal. That's what tempering is for. Now, going out on a limb, praying for different things from that god could color said god's psyche and change their behavior; I believe it was stated in the Live Letter expansion that the reason the primals are so hostile to us right now is because their worshipers are praying for salvation in a hostile and dark time (amalj'aa want Ifrit to help them conquer more land, kobolds want Titan to protect them, ixal want Garuda to destroy their enemies, etc.).

Since it's the exact same deity, probably not. But if you came up with a new one...