I noticed there is an option allowing one to paint on multiple bones together:
The document says:
Paint on all selected vertex groups simultaneously, in a way that preserves their relative influence. This can be useful when tweaking weights in an area that is affected by more than three bones at once, e.g. certain areas on a character’s face.
But how can I select more than one vertex groups?
Ctrl+LMB selects only one bone.
Ctrl+Shift+LMB on a bone doesn’t work. The mesh properties panel lists all the vertex groups, but I can only select one there as well.