An intergalactic, Cross-Time teleporting, interdimensional Hell Lord could probably show up in several titles; it is a lot more rational than Wolverine or Spider-Man showing up on multiple teams. It also 'solves' her as an editorial OP problem; if a plot requires a psychic or other minor pest to take down the team, Illyana could simply teleport away first, before the villain ambushes the remainder of the team etc.
For that matter, every mutant could be given a minor "spell" like
"Illyana Rasputin
Lady Magik, I'm in fear
Please gate me away from here"
We've seen that, like all Hell Lords, Magik can hear her name being spoken, and like other Hell Lords, Magik should be able to send her energies and attention to petitioners (TNM v1 #39 & others hearing her name spoken, #29 casually rescuing Sam from the stratosphere with her back turned, while interogating a prisoner in Limbo.)
It might be really boring to Illyana, but her "Killer App" is to spend time in Limbo Mission Control using scrying mirrors to monitor teammates, spy on enemies, and teleport people and materiel, since such action can be done outside of time. (See her abduction of Moira as medical support personal for the Mutant Massacre in TNM v1 #46.) Given the variable time ratio of Earth to Limbo, in emergencies she could even do it in "frozen time”, noting that she spent seven years in Limbo during seven seconds on Earth back at her Origin in UXM v1, #160.
However, regarding being on or at the disposal of every team, I don't think she herself can replicate through time-travel; Hell Lords & Beyonders are Invariant, and can't overlap themselves in time.
(Illyana the Hell Lord has never overlapped herself; she's only overlapped her uncorrupted 'little snowflake' self, and only in Limbo/Inferno. Until Bendis, Stepping Disks had never been used to overlap people with themselves, which typically meant travel to before their birth, or into gloomy future dystopias, since the people in question had not made their contributions to goodness, as in "It's a Wonderful Life".)