Good veggies include cucumber (you know this already;-)), yams (this is highly nutritious), squash such as zucchini, and peas. Blanch all of these first to kill bacteria and soften them. Squish the peas out of the little shells (=skins, not meaning the pods).
I've never heard of feeding veggies "too much," so maybe put a piece of one or two of these in each week? Be careful to remove any uneaten after a day or two, or they can fungus and rot.