Eternals' biggest story won't happen until at least MCU Phase 7
While there are rumors that Eternals 2 could adapt Marvel Comics' Judgment Day, the massive crossover event shouldn't happen until Phase 7.

While there are reports that a second Eternals movie is in development for the MCU, it's still too early for a potential sequel to one of Marvel Comics' biggest stories involving a family of immortal heroes. Some rumors have even teased that the next Eternals movie will be an adaptation of Marvel's Judgment Day crossover event.
While there hasn't been any official confirmation that Eternals 2 is in theaters, comments and reports from the cast of the first film strongly suggest a sequel is in the works. Likewise, a producer at Marvel Studios has confirmed that the Eternals will be returning in some way. However, Judgment Day isn't the story to draw inspiration from immediately after the first film's criticism and the current state of the MCU in general.
Eternals' Judgment Day Story In Marvel Comics Explained

Published by Marvel Comics in 2022, A.X.E.: Kieron Gillen and Valerio Schiti's Judgment Day is an epic crossover event featuring the Eternals, Avengers, and X-Men, all at war. However, their conflict was interrupted by the resurrection of one of Earth's first Celestials, who threatened to burn the world to the ground if the planet's population was deemed unworthy, either individually or collectively. Featuring several heroes who cast cosmic judgment on the Legacy while searching It's a high-stakes, desperate event for ways to save the world, and the Eternals are right in the middle of it all as they try to change a core aspect of their existence. This epic storyline should be saved for Phase 7 of the MCU.
Judgment Day brings together several different heroes, whether they are humans, Eternals, or mutants. As long as they care and call Earth home, they can all go all out for this massive cross-border collaboration. So it's a truly epic event that deserves to be told on the big screen in some shape or form. However, there are several other events that have to happen in the MCU before Judgment Day can be all it should be.
Why Eternals' Judgment Day Cannot Happen Until At Least Phase 7

Since one of the main criticisms of the first Eternals was that none of the heroes had enough time to fully flesh out, it didn't make much sense to throw more heroes and teams into it. Instead, Eternals 2 should focus more on the Eternals themselves, while continuing to maintain tension with their creators, the Celestials. Once viewers have had more time to explore the new team of heroes who have protected Earth since the dawn of civilization, then Crossovers with other heroes can and should happen.
However, Marvel Studios shouldn't just ignore the Avengers and X-Men. With MCU mutants already starting to appear, a film adaptation of the Avengers' war against the mutant's greatest heroes against the Phoenix Force definitely deserves a mention. Also, the X-Men should be fully integrated into the MCU by Judgment Day, since a big part of the conflict is the Eternals discovering that the X-Men share DNA with the Deviants. In any case, Judgment Day will be a dynamic trilogy finisher rather than a direct sequel to the first Eternal. Also, the original story has no alternate realities or variants, so it should be saved at least until after the Multiverse Saga ends.
Judgment Day Would Be Perfect For MCU's Eternals...But Will It Get That Far?

No confirmation on what's next for the MCU in Phase 7, other than Phase 6 and the Multiverse Saga. Likewise, the first Eternals' split did raise questions about whether Marvel Studios would develop a sequel, opting instead to have the hero pop up in future movies or in larger events like Avengers: Secret Wars. So reports of Eternal 2 are somewhat surprising, although it seems exciting to see Marvel Studios Committed to continuing their story.
While it shouldn't be the basis for Eternals 2, Judgment Day is perfect for future immortals. Combined with previous theoretical Avengers-X-Men crossovers, the MCU could have a dynamic team-versus-team conflict trilogy starting with Captain America: Civil War. First, the Avengers fight each other, then the Avengers fight the X-Men. Then, Judgment Day will put the Avengers, X-Men, and Eternals all at war before uniting against a cosmic threat that threatens them all. It's a fascinating idea for the MCU and the Eternals franchise, though there's still a lot of ground to cover before something like Judgment Day can successfully land on screen.