I've had such an idea since before Beyond Earth came out, though I now view the hybrid system as superior to and likely incompatible with it.
It is called
Discovery, and it is built on a possible response to the Progenitors.
Adherents to the affinity would be fascinated by the fact that humanity is not alone in the universe, that a more advanced civilization exists.
They would idolize the Progenitors, from what they could learn of them, as a perfectly developed civilization - the peak of knowledge, culture, and philosophy.
As such they would emphasize studying and emulating Progenitor culture, technology, and even possibly genetics, dismissing other paths as dead ends to perfection.
From this they would discover Psionic technologies, and their armies would have a theme of adept support units and experimental, somewhat fragile units using technology that is not fully understood.
Their cities and general aesthetic would have a sort of pseudo-religious theme, ideally references the Xcom EU Ethereals and their Temple Ship.
The colors of the affinity would be a deep purple and white.
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To fit the hybrid system, I think a pairing of two affinities should be maintained to keep distinct themes possible.
In order to truly fit a new affinity would need to have believable and sufficient influence and differences from both its parents, provide a coherent and unique outlook on humanity's future, and not overlap with existing hybrids or primary affinities to the point of redundancy.
Nothing I've seen for a fourth affinity meets those standards.