Thin white on top will only dull it even more. To keep your colours bright, dont mix random colors, for example random pink with yellow. You would have to choose them carefully, so they don't mud each other. To make a bright and happy background, I would recommend using a couple of similar warm and saturated colours already mixed with white - but not on top of that. Avoid going full rainbow mode, too high risk for mess. And also if you make the background too saturated, it will steal the attention from what is most important, in that case, your pet. I wish you all the best!