I think it’s a great idea, and find they are better used than a screened in porch is.

Is it on the front of the house or the back and how will it change the look of the house?

What will you use the 4 season room for that you don't already have space for?

What is your climate? I find with climate change there are so many more mosquitos and other bugs and I am greatly appreciate the idea of a screened porch.

Lots of variables. Is it on slab or deck? Are the walls just screens?

What you do for the enclosed room is also influenced by the architecture of the home.

There is a company that fabricates panels to be inserted into the openings.

https://ezporch.com/

A 4 season space will need heating how is that going to be handled . Converting a porch to real living space is not a simple add windows job. I need more info from you and pictures for sure. Waht do you want to use the space for as a 4 season space ? I do not agree that the use would be better , better than what ?

Most screen porches are on minimal foundations with light framing. Converting them to a part of the house is often essentially starting from scratch except maybe saving the roof

I'm falling in with most responses here that it's not worth it. The whole point of a screen porch is to be outside without bugs. A 4 season room is essentially an addition to your house, not an outdoor space. So the questions Kendrah asked are what you need to respond to.

Personally, unless your house is tiny and you're bursting at the seams, I would much rather have a screened porch than a (basically) sun room.

Most screen porches that are converted to sun rooms are hard to keep warm in cool weather and cool in hot weather. They tend not to be used as much as the owners expected. You could add a wood burning stove to your porch and get more use out of it.

My FIL has a 3-season room, which is basically a screened porch where the screens can be replaced with glass for the winter. No heat, no A/C, but overhead fans. It's in NYC, and tends to be reasonably comfortable much of the year. Depending on the climate, house orientation, and other gory details, that is something I can see worth doing.

OP has gone maybe working . But we need answers .