Overwrite ComboBox menu paint?

I want to add some painting for each row in the ComboBox control (closed and opened state). A simple additional painting doesn’t help as the combobox overlays outside it’s regular dimenions. How to do that?

That’s the comboBox’ popup menu that you want to customise.
So you have to create a lookandfeel (inheriting LookAndFeel_V3), and override the methods that are in PopupMenu::LookAndFeelMethods.
then set this lookandfeel to your combobox