How to refineMesh for a given y range?
 

I am thinking that refineMesh (with some simple refineMeshDict) can double or quadruple my cells with y in some range, but can't find any internet examples. So, how is this done?

The challenge is that I want to match two faces for one at the interface as in the images below (I could instead use mergePatchPairs in blockMeshDict, but prefer to later use refineMesh or something simpler).

Starting Mesh:
https://i.imgur.com/VQOZhu7.jpg

Ending Mesh for Doubling:
https://i.imgur.com/9CiNZP9.jpg

Ending Mesh for Quadrupling:
https://i.imgur.com/yWOld20.jpg