Relicensing a project from GPLv2 or later to AGPLv3 or later

Switching from GPLv2 or later [1] to AGPL [2] is perfectly legal. But if it is not your own project, it is often considered rude.

This does not relicense the original code, it just sets the license of new code and of the project as a whole. The old code stays GPLv2+, but when it is combined with the new code under AGPLv3 (or later), the combined project will be under AGPLv3 (or later).

However switching from GPL2+ to AGPL3(+) without consensus of all other contributors is considered rude, because it could prevent some of the original authors from using future versions of the project. Their professional use of the project might depend on the loopholes in the copyleft of the GPL.

And the ones you will want most of all as users of your fork of a mostly discontinued project are the original authors, because that can mend the split between the two versions.

This question came up in a continuation of a widely used package whose development seemed to have stalled. The discussion was unfocussed, so I decided to write succinct information for all who might find themselves in a similar situation. I will not link to them, because I do not wish to re-ignite the discussion through an influx of rehashed arguments.