If OP is not a Schengen citizen then they will be registered as an overstayer and could be prevented from returning or getting an ETIAS next year.
Since Britain looks like having a hard Brexit it shouldn't affect entry there as they will no longer be able to access the Schengen database. However if by some miracle a hard Brexit doesn't happen an overstay will be visible to the Border officials.

Its no more a good idea to say OP will have no problem staying for 4 months in Schengen than saying I could stay in the USA for 4 months without a problem.
Please don't encourage people to break the law. They will face the consequences not you.

Subject of the post is three or four months -)

The OP needs the right to stay but that doesn't have to mean Schengen. The OP could be Irish

I don't see any reason she couldn't visit those places from Italy. She's talking about four months. You could easily to to Switzerland, Austria, etc. for a long weekend or 4 days or so. Or southern France easily, but you could easily do a long weekend in Paris with short cheap flights nowadays.

But that means looking at a budget airline, say Easyjet, and check their direct routes. Milan as flights to London, Paris and AMS. From Naples, they have flights to many locations, that's kind of weird actually, but it must be amajor hub of theirs. You can fly to Austria, Prague, Paris or other French cities, and even to Greece, direct. But I doubt if Naples is the idea of a place she wants to live four months and then if you were in the north, you could go to Austria by train. Venice has tons of Easyjet flights also, and that is more realistic I haven't been there, but I presume maybe there is some place that isn't tourist central where you could live there reasonably? Maybe not, maybe Milan would be a better idea, you could take the train to Switzerland or France from there, maybe Austria?

Even if she is Irish, or other non Schengen EU she can only stay in a single Schengen country for 90 days before she has to be registered with the authorites, and earlier if she wants to work.

Milan would be an efficient choice. Whether it is too large of a city for this person, who knows?

Decent flight options from the airport and close to Milano (1 hr by train) and a bit smaller, though not "small": Torino. It has quite an elegant historic center with some interesting museums and is close to good hiking if that's of interest. Plus excellent wine country nearby. And great cheeses.

https://www.nationalgeographic.com/t...s-turin-italy/

That clock restarts every time the OP crosses the border. But I've never heard of that law being enforced and even if it was the most the EU allows is a small fine.

Milan would be an efficient choice

Traveler_Nick, I thought the 90-day rule was 90 days in any 180 days, not being able to start over just by crossing the border. She would have to be out another 90 days before being able to come back. This is without a visa. Is this not correct?

No we're arguing if the OP is an EU citizen. If so the OP technically legally needs to register her presence if the stay exceeds ninety continuous days. No visa needed.

The thing is while it's true EU citizens are supposed to register many don't. I'm not talking about backpackers spending a few weeks but people with homes and cars.

We're going round in possibly irrelevant circles without more info from OP, who has not yet returned.

Traveler_Nick, I didn't have the impression the OP was from Europe, so it seems unlikely that she's a EU citizen.
nonconformist2, you're right, we haven't heard anything more from the OP, so we don't really know.

I know but until the OP returns all we can do is go around in circles O:-)

Wonder what happened to Vanessa?

I'll give you three guesses...