Cox love the fit. Slight criticism- while the trousers and jacket looks "lived in" ; the shirt and tie are on the neat side. Maybe a linen shirt and knit tie? White linen square with coloured border? Warning: Spoiler! (Click to show)
The tie is actually somewhat textured, almost like a grenadine grossa. You're right about the shirt. I don't have a white linen square with coloured border but I should, and yes, it would look good here. Although I do like the splash of colour provided by this mauve square too.