I spitballed a few different genres that might work, what sorts of adventures they’d be suited to, what would be suitable years, and how it all might fit together. I built on plot threads in the original game and used some ideas from Chrono Cross, though this sequel assumes Chrono Cross doesn’t happen. Here’s what I came up with, in the order that the player would visit the eras:

2400AD
Genre: N/A. Functions similar to original game’s End of Time, a hub through which to travel to other eras.
Summary: Crono and co. get yanked to Chronopolis by Balthazar who reveals that a change in the timeline, tied to their actions in the previous game, has resulted in the Kingdom of Guardia never being founded, and thus, Crono and co. never being born, undoing the defeat of Lavos. Chronopolis exists outside time and is protected from these changes. Balthazar traces the timeline divergence back to the year before the founding of Guardia and so sends the party to 1B.C.
Era-specific party member: N/A.

1BC
Genre: Sword And Sorcery
Summary: The party investigates the era and finds something that wasn’t there in the original timeline - a vast chasm in the Earth from which monsters have been unleashed on the populace, creating a regional instability that prevents Guardia from ever forming. The party defeats Dalton and re-seals the pit. An era miniboss is a snail monster that leaves behind the Rainbow Shell.
Era-specific party member: A glass cannon barbarian type, fast and with a huge axe, specializing in basic attacks and techs that do fire-based physical damage.

1500AD
Genre: Dieselpunk
Summary: The pit was closed, but Dalton’s fuckery has had knock-on effects on the timeline. Porre, now a global military power, is conducting underwater mining operations to strip the wreck of the Black Omen. If allowed to complete this, the technology they gain from it will enable them to become a hegemonic empire that triggers a global nuclear conflict around 1900AD, so the party has to stop them. Marle has a plot arc where she learns that Guardia fell to Porre in a military conflict around 1100AD and must come to terms with the fact that, for the timeline’s sake, she cannot change this history.
Era-specific party member: An aquanaut who wields a spear gun. Well-rounded stats and water-elemental special attacks.

1800AD
Genre: Cyberpunk
Summary: Last section of the game’s first arc and the last step to repairing the timeline Dalton broke. The city of Arris (the origins of Arris Dome in 2300AD) is, due to timeline changes, going to succumb to a megacorporation coup that failed in the original timeline. If the coup succeeds, the megacorporation will carry out a strip-mining project that will awaken Lavos before the party can defeat it in 1999AD. The party has to raid a corporate headquarters with the help of underground hackers and expose the coup plot.
Era-specific party member: A hacker type who specializes in techs and special attack/special defense. Lightning-elemental attacks.

The timeline is fixed, and all seems well, when the crew suddenly gets pulled by a Gate to…

2500AD
Genre: Biopunk
Summary: One of the world’s first interstellar expeditions encounters an inhabited planet. Its plant-like sapient inhabitants have developed ultra-advanced biotechnology that they use in place of machinery, having integrated their civilization seamlessly into the biosphere to create a sustainable post-scarcity utopia. However, one of their leaders reveals that they can feel the presence of a nascent Lavos-spawn within their planet, one that landed millennia ago. It is still a long time from fully awakening and destroying their world, but recognizes them as a threat and is using its ability to guide evolution to turn the biosphere against them, an infection they can keenly feel. Several regions of their planet have turned into overgrown, malevolent biomes teeming with monsters, and one colossal beast roams the planet, ravaging their civilizational centers. The party must defeat this beast, after which the planet’s civilization will be able to recover enough to organize against and kill the Lavos spawn. The first game’s theme, the implication that the Planet created the Gates so that the party could defeat Lavos, is expanded upon here, with the implication that the aliens’ planet pulled proven heroes out of time to defeat its own infestation.
Era-specific party member: One of the plant aliens. Primarily specializes in healing and buffing/debuffing, with a secondary focus on damage-dealing special attacks. Shadow elemental.

3000AD
Genre: Military Sci-fi
Summary: Humanity has become an interstellar civilization. It has discovered that Lavos spawn are far more numerous than anybody anticipated - most inhabitable planets have either been destroyed by Lavos spawn or have had one implanted. Humanity has advanced technologically to the point that it is capable of destroying them, but it’s fighting a losing war of attrition. Recently, an ancient alien facility has been discovered on a post-Lavos planet, since strip-mined, and the facility itself appears to postdate the emergence of the Lavos spawn. The facility may hold the keys to learning the origins of Lavos’ species, but it is guarded by ultra-advanced robots and bioengineered creatures, and breaking in to unlock its secrets will be a dangerous mission. Once the facility’s core is breached and its archives studied, the truth is revealed: Lavos and its spawn are the creation of an ancient alien race, used to preemptively obliterate any potential resistance before planets are stripped for resources.
Era-specific party member: A soldier in heavy power armor. Slow, but nigh-indestructible and hits like a truck. Lightning-elemental, though some techs do Fire damage.

3100AD
Genre: Space Opera
Summary: Crono and party appear on the flagship of a vast interstellar battlefleet, brought there deliberately by a “beacon” device built into the ship’s bridge. Spurred by the discovery made with the party’s help in 3000AD, Earth has spent the past century working to locate the source of the Lavos species and assemble an interstellar fleet that could meet the threat. The source has been identified as a planet belonging to an ancient and advanced alien race. The planet’s entire mass has been converted to a monstrous biomechanical factory where new Lavoses are continually being produced - and recognizing the threat of Earth, the alien race has begun accelerating production. However, they have also grown complacent and let the planet’s orbital defenses stagnate. Earth has one chance to strike before the enemy can reinforce, punching a hole through the orbital defenses and surface to insert Crono and co. into the planet, where they can fight their way to its heart and destroy it to end the Lavos threat at the source. Gameplay is functionally very similar to the original game’s Black Omen, with a long and difficult climactic dungeon ending in the game’s final boss encounter.
Era-specific party member: None. This is just the arena for the final showdown.

I’d love to actually make this, but 1) I’m busy with other shit, 2) I’ve done just enough SNES ASM hacking to know that I have absolutely no patience for it, and 3) Square-Enix is infamous about C&Ding Chrono Trigger fangames