Dogs can eat vegetables more than cats, and they have vegetarian dry dog food. However, NEVER attempt to do that with a cat, not that they'd let you thank God for that!! Cats need things like Taurine and they need massive amounts of protein or they will DIE. The teeth of a species will tell you what they should be eating, and cats have very sharp pointed teeth because they are meat eaters.
KNOW THIS: Humans can eat vegetarian, our teeth are designed for it and our long intestines demand this, but a cat's intestine is short and doesn't get clogged from eating a healthy meat diet and thus they don't get the major build up of toxic waste on the walls of their colon like us humans do. Cat's teeth will tell you they are not plant eaters, although they DO enjoy eating plants, catnip, and grass. My cats graze on long fresh tender blades of grass every day and they fight over who gets the first batch. But that is just a salad for them (and don't bother getting the kind at petsmart, my cats snub their noses at that, it's like processed grass of a sort, all the nutrients and fresh smell of grass is almost absent from it). use the long blades that grow by the corners of the yard, the blades that that mower doesn't reach.