I suggested 3 due to the character limit in the message. You could probably fit 5 if you devoted your entire message to it. In my case, Garuda and Quetzacoatl would not be available at the same time. I'm water element, so usually I'd be running Garuda. But during a Thunder event, I might run Quetzacoatl. Since Quetzacoatl would hardly ever be out, I should probably just replace her in the message with Anzu.
After this event, I'll probably add my newly LB4 Apocalypse and Phoenix to the list and equip them to my formations to be a more versatile friend.
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On further investigation, it seems that the number of friends available is fixed (maybe at 6?). If one of your available friends doesn't have a primary eidolon for a given element, that slot is wasted! So aim to cover all 6 elements with your primary eidolons. Failing that, use the double-element eidolons to cover all 6 elements with 3 eidolon, then use the 3 remaining slots as you see fit (unless you have a better eidolon that will be masked by one of those double-element eidolons).