Staying In Switzerland for 4 months

From the U.S. Dept of State:
https://travel.state.gov/content/travel/en/international-travel/before-you-go/schengen.html

Not easily.

"I am coming from the US." - yes, but are you a US citizen? I guess you are.

"Can I go to maybe France or Germany for a few days at the 90 day mark" - no, for two reasons:
(1) The limit applies to the Schengen Area as a whole, which includes France, Germany and all other countries surrounding Switzerland. You would need to exit the Schengen Area, for example go to Croatia, or the UK.
Map of the Schengen Area: https://img.washingtonpost.com/blogs/worldviews/files/2015/06/SchengenArea-2300.jpg
(2) The limit is "90 days in any 180". If you leave it does not reset the clock, it just stops the clock and it carries on when you return.

You would need to apply for a Swiss residence visa, and you would need to get this before you arrive in Switzerland. I suggest you contact your nearest Swiss embassy or consulate.
Are you being paid? If you are, this counts as work, and your visa would have to allow for this.
Swiss immigration rules are at least as tight as the USA.

IMHO a US (or any other foreign) government website is just hearsay, they don't write the laws, the Swiss government does. That website wbfey1 posted is factually wrong. It says:
"Spend three months in the Schengen area during any six-month period, you must wait another three months from the last date of departure from the Schengen area before you can apply to enter the Schengen area again without a visa."
The limit is "90 days in any 180", NOT "3 months in 6 months". And you can re-enter 181 days after your initial arrival (because then there are only 89 days in the last 180), NOT "three months from the last date of departure from the Schengen area".

Good luck with that...it sounds impossible. I say that because my daughter married a Swiss man and supposedly qualified for the easy-to-get Family Reunion Visa (she moved to Geneva). There were many tears and lots of teeth gnashing attempting to get that "easy" visa.

It sounds like you need to trim your house-sitting assignment to 89 days.

" I know this topic has probably been discussed before but I was hoping for some new info or insight."

Unfortunately for your plan, there is nothing new on this front to report. And in Switzerland, expecting anything or anyone to be lenient on the rules, is generally not going to have a good outcome.

Every so often someone spams the forum with offers to sell a passport. Mayhaps you could buy a Swiss "passport" from one of those fine vendors. What could go wrong?

I wrote to the Swiss consulate and got the info I needed for my stay. For everyone who tried to be helpful, thank you. For those that felt the need to be snarky, really not necessary or nice.

Snarky? Where was the snark? If the responses did not offer ways around a problem of your own making, that isn’t being snarky.

Norma, I believe the OP was referring to the post by fasteddie, which was indeed snarky.

@chefkim68 - could you share the info you got from the Swiss authority?

Oh, I see. I didn't find that snarky, just sort of smart ass-y.

One person's smart ass-y is another's snarky. I always assumed they were one and the same, but there may be fine shades of definition I am unaware of.

Words to live by.

Thanks Nancy! LoL 😁

...and??....

I wrote to the Swiss consulate and got the info I needed for my stay.
For everyone who tried to be helpful, thank you. For those that felt
the need to be snarky, really not necessary or nice.

And for the benefit of those who come after you, could you tell us what the advised?

Yes, that would be helpful to many. Our daughter may be attending grad school in Switzerland next winter and we might like a nice long visit there.