Built-in shader cutout+transparent

Is it possible to have a shader that uses both cutout and transparency?
I need a classic built-in shader that uses cutout.
But I also need the “full-opaque” parts to be transparent and not affect the cutout.

In practice I have objects with standard cutout shaders.
Now I’d like to manage their transparency when the camera hides the player.
Using the alpha of the albedo modifies the state of the cutout, but I would like real transparency.