Then you can also extrude the modified side face.
However, if you want to make other changes, it is better to create a custom geometry. The side face is also a custom geometry.
UPDATE:
In the Collection
Collection of examples from discourse.threejs.org
you will find (2017) a simple example of a self-defined BufferGeometry. In newer revisions of three.js you need to replace .addAttribute with .setAttribute
https://hofk.de/main/discourse.threejs/2017/Indexed%20BufferGeometry/Indexed%20BufferGeometry.html