Attached is an example of few notes in piano-left-hand (bass clef), but in three voices. The colored rest in the .png from Dorico is the rest I need to move horizontally a bit to the right to avoid collision with the note-stem.
Engrave mode does not give me a handle for this rest in Note Spacing. Thanks, all!
Yes, I have looked at these previous topics.
Go to Engrave mode
Open the properties panel
‘Offset X’ should give you what you want
Engrave / Note Spacing ON / Alt + arrow keys should do the job (see the image attached). Your specific case seems to be somehow too difficult for poor Dorico because of the “overlapping” items. You probably have tried to first move the notes a bit away, if they have handles, and then move the rest, if it now has a handle, and then move the notes back to their correct position?
It probably should, but at least my copy of Dorico 1.1.0.100 does not move a rest (or a note or a dynamic marking) horizontally when Engrave / Offset X is applied. Nothing happens. Offset Y does work.
Engrave / Offset X does move a lyric syllable, for example, but as stated, not a rest, note or dynamic. Is this intentional? If not, I hope it will be fixed soon. 
You’re absolutely right. I checked with a bar rest, for which it works, but appeearantly not with other rests. Note spacing should be the right solution.
I guess it is intentional for items that have another way of adjustment - such as note spacing for note and rests, and ‘start offset’ for dynamics. It can be a bit confusing that non-functioning properties are visible, so I hope the panel becomes a bit more context sensitive in the future.
I will look at all this this week. As I’ve said before, this particular song cycle (Scènes et Mélodies by M. Caillebotte) with its multiple-voices in one stave, odd beaming, etc. is a brilliant work for testing the limits of any music notation software.