Are you making other changes? You have that strange builder mix of traditional elements (quoins, arched windows, columns) and modern elements like casement windows. You need to decide what you want to lean into. If contemporary you could fit a large rectangular transom where the half round is now, if you are trying for traditional a square accent window could be installed higher in the peak.

Have you talked to a stucco contractor yet? EIFS isn't hard to work with, but does take someone with some experience in the substrate is all. And you are wanting to enclose that space and just make it wall? The difficulty will be in blending the old vs. new stucco lines, but not impossible.

There are a lot of architectural details going on. Are you willing to post a picture of your entire house for context?
The appropriateness of this window really depends on how it fits in with the rest of the house.

Thank you for your thoughts. The main reason we want to possibly remove the top half-moon window is the sunlight and heat that overpowers this 12 x 13 room. It is used as a bedroom. While we can do room darkening shades, the top window would be covered anyhow. There us film on the outside windows but it appears to be cracking. Plantation shutters were ridiculously expensive due to the top arched window. As requested, here is a full frontal view of the house. i am also including an interior view. The window just overpowers the room. Having just moved in, we are trying to prioritize projects. I would imagine windows are down the road as they are 25 years old. Thanks!

This is our house. It also has a half moon window but a different roofline. It might give you some ideas. We do have Norman shutters which I like.

Lovely home. The stone adds a special dimension. Interior plantation shutters? If so, I did not realize Marvin made shutters. I

Norman shutters, not Marvin.

It would be much cheaper to replace that assembly of windows than it would be to mess with the stucco. That or some sort of applied solar control film as an intermediary.

I added plantation shutters to the front two rooms. Thank you,Shasta, for the idea! It was a perfect solution. They help with insulation, look great and we now have options to control light.