Hi !
Yes, sure, Beautify is compatible with Volumetric Fog & Mist. For a best result, you may want to add Volumetric Fog & Mist after Beautify in the camera's stack of scripts.
To reduce or cancel fog on certain areas, you have 3 options (in order of difficulty):
1- Use Fog Void. This option eliminates the fog around certain position, for instance, around the character. You can specify the position, size and also the shape of the void (square or spherical).
2- Use Fog Volumes. You can add any number of fog volumes on your scene and specify a different alpha value for each one. Just drag and drop the Fog Volume prefab to the scene and customize the location and size of the collider. Note that the alpha value will affect the entire fog.
3- Use Fog of War. This feature allows you to use a texture whose alpha channel determines the transparency of the fog at any position. For example you can have a texture of 1024x1024 mapped around world position 0,0,0 and with a world size of 1024x1024 so each alpha value of the texture maps to a world position. Check the fog of war demo scene.
Let me know how it goes.