People make all sorts of claims about what increases metabolic rate, because most of us ( me, me! ) like to eat and the higher your rate, the more you can eat without gaining weight. However, most of the claims are neither supported nor denied by good scientific studies.
Exercise and having more lean tissue (from weightlifting for example) definitely raises rate. Stimulants definitely raise rate (nasty side effects included for free). Some hormones (thyroid hormone, growth hormone, cortisol, and anabolic steroids for example) raise rate too (along with other actions).
I've never seen good evidence that being vegetarian, or vegan, or raw, or Atkins for that matter, does or doesn't affect rate. However, a vegetarian's diet is often less calorie dense and has more fiber. This can decrease the absorption of the calories you eat, so you can still eat more calories without gaining weight. It definitely increases the volume of food you can eat without gaining weight.