How to create an irregular shaped dome?

I started using SketchUp recently and this is the thing I can’t find a way to do. I want to create kind of a dome with this base’s shape. I’m able to make a regular, circular dome but I wanted to extend it to the rest of the base.

Something along these lines?

Yes, that’s it. The way I tried to do the surface was always uneven

I Rotate/copied half the top perimeter up to 90° and added an arc from the top to the side.

I scaled those curves down a bit since yours appears to be flattened.

Then I used Curviloft to skin over the “dome”.

Explode the groups Curviloft makes and soften the edges.

You could also use basic tools

and another option with Soap Skin Bubble plugin

Thank you for your methods. Soap Skin Bubble was really what I was looking for not only for this but for other stuff I wasn’t able to do. I just wanted to know if I can use it to do the same thing but with a hole in the center and it end up kind of like an irregular donut. It always does the whole area of the outer lines. (I’ll create another thread if needed)