What if Two Incarnae want to Exalt The Same Person?

[The Random NPC]

When two companies wanted to hire me at the same time, I would choose which offer to accept.
If two women were interested in me at the same time, I would choose who to date.
When two D&D groups want me to join them for a Saturday afternoon game, I decide whose house to drive to.
When two colleges admitted me, I chose which one to attend.

Why would this be any different? [And how?]

If two different states want to try you for crimes, you don't get to choose which state tries you.