I know that this is an old post but of course, people will continue to find it on the Web and be interested in possible solutions, so I thought I'd add a couple that I have used:
Sesame oil (especially toasted version): This works great to doctor up a bowl of bland soup, just a little bit is needed. Actually any nut oil is good, but the sesame is strong and you only need a tiny bit. It's also healthy.
Garlic: I started keeping a jar of crushed garlic in my refrigerator for these kinds of uses. Again, you can add just a bit to your individual bowl this way. Otherwise, add a lot of garlic to the pot. You can roast or sautee it first. When I make soup stock I usually use at least two entire heads of garlic. As long as you don't smoosh the cloves together (which creates a chemical mash-up that produces the harshest flavor variant), it will produce a wonderful effect.
Roasted Bones: I wasn't sure if the person was attempting to stay vegetarian with the soup but it doesn't say so. In my experience with making broths, which is extensive, I have found that the absolutely best and most important ingredient is bones which have been cooked or roasted (i.e., from your roast chicken or whatever). Raw bones are commonly used but you are wasting the maximum flavor potential in them if you don't roast them first. And you ideally want rather a lot of them. So to doctor a soup, you could buy a pack of soup bones at the market, roast them, and throw them in there. Ham hocks etc. are well known solutions as well but I've found them so variable in flavor and saltiness etc. that they are a bit tricky to use, in my opinion. Note that you can mix bones too, such as from a chicken and beef ribs; just don't include fish bones with other bones.