What Barbara describes as the classic mirepoix formula produces a stock with balanced flavors and nothing unexpected. It is the formula to use when you need the stock to use as an ingredient in another dish, or when you don't know how you'll use it. (A lot of professional cookery depends on achieving consistent results.)You can use other vegetables and vegetable trimmings in soup if you think you will like the flavors. Parsnip, which has already been mentioned, is very good in chicken or turkey soup, but you might not want a strong flavor of parsnip in the stock used to make a velouté sauce. More than a very small amount of broccoli or cauliflower could contribute a cabbage flavor, which is undesirable in just about everything else. Even if you are making a boiled dinner, in which cabbage is a typical constituent, it is better to remove a cup of stock from the main kettle and use it to cook the cabbage separately.Asparagus can contribute a peculiar green color as well as a distinctive flavor. The color wouldn't be noticeable in a brown stock, but a greenish chicken stock would be strange. (Incidentally, inclusing a small piece of the skin of a yellow onion gives chicken stock a good color. Too much turns it a funny brown shade.)Even using different proportions of the classic ingredients can have an undesirable effect. One of my aunts always used much more carrot in soup stock most cooks would; the result was a stock with a beautiful but oddly dark color and an objectionable sweet flavor. Leeks, which are acceptable (being like onions) contribute a smoky flavor that is very appealing in soup but not wanted in every dish for which you might use a chicken stock.For that matter, with a beef stock, the type of beef used makes a noticeable different in the flavor. For example, the stock remaining after making boiled beef has a markedly different flavor if the beef is brisket instead of, say, chuck.