Hmmm... you know, there are arguments pro and con for either way.
Juices are very concentrated, so as long as it's fresh squeezed and not sitting around waiting for you to drink it, multiple drinks are better. If you take them prior to or with meals, you also get the benefits of their wonderful enzymes to help with the rest of the meal.
You can add lemon juice to the carrot to help with meals too, in fact, add ginger juice! Carrot-apple-ginger-beet-lemon is SO tasty and cleansing, just about the perfect cleansing cocktail. :)
You get more of a flush effect on the liver by taking at least 2 oz of beet juice all at once on an empty stomach. And if your digestion is weak, you don't want to snack too much, even on raw juices, in between meals, so sometimes doing meal replacement with a large glass of veggie juice is better.