When was it built? 1960's-1970's? If the original architect's name is on the plans at city hall, you can see if they'd be interested in designing an addition. This is a contemporary design that is probably not going to be easy to build a second story on. Consult a structural engineer for advice.

I wonder what the builder was thinking when he fabricated those flared walls. I don't see any functional advantage. Are the walls at an angle in in the interior?

Would you be open to changing the walls to conventional 90 degree vertical?

Can you raise the house so that the existing first floor becomes the second?

"any thoughts on how to build a second story that works with it aesthetically?"

Nope.

Can’t see any way to add a 2nd storey without rebuilding the 1 st one maybe an addition to one side.

It was built in 1954. I actually really like the look of the house, pulse it would be cost-prohibitive to make it look normal. The interior walls are 90 degrees. We have no idea what secrets the space in between holds. My builder says he can build up; I just need to decide on what the exterior will look like.

Thanks for info. How about continuing the slanted walls up to form full size pyramids? Would that give you the second story space you are looking for? Or you could duplicate the first story completely, stacking a second one on top of the first. With photoshop, it'd be possible to mock up both ideas to see if they are workable or laughable. Maybe celerygirl or groveraxle will see your post.

You could take photos of the other three sides to add in the comments so you get more ideas from other people.

Teardown mansard cabin is what it’s called. There is no way to add anything to that without rebuilding everything. Including the foundation that won’t support a second floor.

Your best bet is to hire a good local architect that can easily gather the information needed to get your desired end results. For help determining the house's style, see Lester Walker's book American Shelter: An Illustrated Encyclopedia of the American Home.