I did not paint him wet-on-wet. This sort of fur colouring - black, red, yellow, cream - is tremendously difficult to paint wet-on-wet. Best possible colour choices for achieving mud, in my experience.
My technique, which is not idiot proof (or at any rate, it is not proof against this idiot) is to keep white off the palette altogether for as long as humanly possible. White is the problem. I try to follow Peter Paul Rubens' advice if I can:
White is poison to a picture: use it only in highlightsI painted his eyes first - to finish because one of the joys of painting a portrait like this is the feeling you have a friend walking with you.
Then I painted everything that was black, or nearly so (the background, for example, is a mix of black and transparent oxide red - it makes the black warmer somehow, without detracting from the dark quality).
Once the black was dry, I painted the nose, tongue and gums to finish, then let them dry and painted in the red and yellow ochre fur with no white on the palette.
My poor friend looked distinctly moth-eaten and to avoid the temptation to fiddle, I turned the painting to the wall until the paint was tacked up but not dry - so I could soften edges and not just leave pale fur sitting on top.
The colours I used were: W&N Alkyd Lamp Black (I use this all the time now instead of Ivory Black and much prefer it); Rembrandt Transparent Oxide Red, Michael Harding Yellow Ochre Deep and Warm White. I only used Titanium White for highlights created by moisture from the dog i.e. eyes, nose, tongue.