I think you even mentioned that the team should start off with some, and have others join in later.
Jean remains as Phoenix for the duration of the Phoenix Trilogy, so we'll get plenty of awesome moments for Jean, and good detail of what it would look like for her to grow as Phoenix. There's definitely moments of self doubt for Jean, esp for when it comes to "Cosmic Rival", as its a
seemingly impossible phenomenon to understand. She questions her bond with Phoenix for multiple reasons as the narratives progress. Jean does eventually learn that psionics, for
some reason, are incompatible with "Cosmic Rival", only energy beings are compatible. Jean also learns her destiny to become White Phoenix is another reason for incompatibility (as she's a human of pure psychic energy, perfect for Phoenix; akin to the former X-Man who is a human of purest level energy, a reason he's perfect for "Cosmic Rival"). Unlike Jean's realization of White Phoenix, as the X-Man transcends into higher evolutions of "Cosmic Rival", he receives the kinds of answers that only spawns more bizarre and at times, frustrating questions.
That's why Giraud would be so instrumental as a nexus of understanding both entities and their energies. Something about their plot I really love too, the chief writer states even tho the Phoenix and "Cosmic Rival" are bitter towards each other, they actually hold answers both sides are in need of. Same thing for Jean and the former X-Man, they kinda hate each other, yet they hold answers each ohter needs.
And YES! I'd love to see Starhawk with Phoenix, that'd be some awesome visuals on screen
I'd also like to see some cosmic escapade that explores their powers in someway, or they even engage in some sort of discussion, something that allows a good interaction between the two.