If they stay within certain tolerances for the shape they were in when they acquired magic! They're reasonably generous tolerances. You can have twice as many arms AND wings AND be lots of fun colors. You could be a mermaid or a naga instead if you want (AND lots of fun colors). Clothes and stuff don't count toward this limit at all.

Unfortunately for the Guests, in this universe "the shape they were in when they acquired magic" is always "the body of a magical girl", and the shape they are in when they abandon a host is "no corporeal body at all." 

Unfortunately, the configuration of this proxy warfare power granting system does not allow for updates in response to feedback!

THAT'S NOT FAIR

...what if they purge themselves of this bullshit magic before they abandon a host? 

Oh, you can't do that once you have it, generally speaking. You don't have to accept it in the first place but you've got it for good after you make enough changes.

Guests can, technically, do that; their whole deal is manipulating foreign magic. Well, half their deal, anyway. 

It's not comfortable. It's not even something it would normally occur to a Guest to try. It's rather like the notion of a vampire spitting out all the blood immediately after feeding on a thrall. Why would you?

They can also refrain from partaking of a host's own magic, if they choose. (Not that this is a natural choice either.)

If a Guest managed to rid itself of this magic, would an outside force restore it?

Nope, if you don't have the magic already and are not a descendant of the population of this planet as of a few hundred years ago the magic system is not interested in you.

Excellent! So a Guest can survive possessing a magical girl, as long as it doesn't try to keep any of her power after it leaves. 

Unfortunately, this fact is not evident from the magic itself. So most of them, uh, do. 

A rare few catalych happen to observe one of these metamorphoses and are cunning enough to deduce the rest on their own, and a few hear about the problem from the others. The ones most likely to survive are the ones who went after after bland boring monsters or influential mundanes at first instead of tasty magical powers. 

But by the time a few decades have passed, all that is left of the advance force intended to pave the way for a massive invasion of Earth is a flourish of exotic new cryptids and a handful of exceptionally lucky and rather thoroughly neutered psychic vampire ghosts. 

...For the record, this is not how an invasion usually goes. 

The few remaining Guests lay low, for the most part, sapping vitality from monsters when chance permits.

The dragon has to go. Avoiding his notice is not especially difficult, for now, but he could likely close any breach they're able to establish before an invasion could build the proper momentum. They encourage and abet several assassination attempts against the dragon, but are careful never to expose themselves directly. If the dragon were to become aware of their presence, death would swiftly follow. So they wait, as decades turn to centuries, seeking an opening.

Eventually, a particularly ambitious host is identified, with a rare and promising power: metamagic, which can affect the dragon's own spells just as the catalych can affect the local magic. 

There's a brief fight over who gets to claim this host. It's higher-stakes than usual, since there's a chance their plans may come to fruition, and they might get to keep her power. If this host survives long enough for a Lexrima to arrive on Earth, it might override that damnable appearance-magic by dint of outright reality-warping.

Eventually a Guest secures for itself the honor of the task, and gets to work.

This host is headstrong, but there is leverage to be found: A lost love, a resurrection denied, a pride that is driven to accept no rule but its own...

Denied? She could totally get a resurrection for Osma! They do that all the time for magical girls! 

Alas, her request did not reach the intended recipient. She can have a curt, formal rejection instead, courtesy of a different agent. If there are any notes of faint dissonance about this message being legitimate, well, the Guest possessing Salem will ensure they fail to rise to conscious attention. 

But why — Osma was a hero, she died fighting to defend the innocent — that's what they're supposed to be all about — 

Osma also had a tendency to ask inconvenient questions. Perhaps he learned something he shouldn't. Perhaps this extremely powerful organization isn't as benevolent as it seems.

But what about everything they've done — 

Her carefully curated information diet suggests it hasn't all been as straightforwardly benevolent as it's made out to be. 

(The campaign of systematized gaslighting takes most of their collective effort to maintain. Fortunately, the Guests have been quietly fomenting conspiracy theories about the Pax Corps for centuries, and the well of lies and half-truths they can draw from is nearly limitless.)

If they steer correctly, they can even get her to agree to a fully willing possession with her mind intact, about as valuable a result as they could hope to obtain.

It's still a few years before they're in a position to implement their plan. 

Some time later, Ipaxalon wraps up a public speaking engagement in Cairo. His next appointment is in the Borlaug building in New York City, so the fastest way to get there is...

Greater teleport.

She's only ever gotten close enough to Ipaxalon to sense this happening once before; she'd hoped to have more chances to get a feel for the process, but she's had to make do. Currently, she's just barely close enough to sense the teleportation spell as it forms.

Her powers boosted by the catalych, she grabs the teleportation effect, simultaneously boosting it and twisting it in a direction it doesn't normally go. Instead of New York City, Ipaxalon can be BANISHED INTO THE AETHER. 

Away with you, dragon. 

And away goes the dragon.

So end all who would rule over humanity as gods. 

Your work is not yet done. You still need access to the means of resurrection possessed by the Pax Corps.