Thicken / offset tilde box to make a straight thickness on each selected face.

[Sergio.D.Suárez]

I have a part as in the picture. I want to remove the highlighted area. 

The tool should have an option to tick, so that the thickness is straight from the face, and through the intersection of the operation with the given solid, the highlighted area can be easily removed.
To achieve this effect, several operations must be performed, one for each face, create several solids and perform features to combine with the final solids.