I've often wished that you could use multiple criteria with the Sumif formula. Sumif can only take one criteria, and if you want to use more than one criteria (with the exception below), you'll need to use array formulas. John Walkenbach has a great explanation of both in his book Excel Formulas 2000 pages 200 - 206.
I've found a somewhat creative way, however, of using multiple criteria in a sumif formula, but is limited in that the match has to be exact, meaning you cannot use greater than or less than calculations. In the main database, take the multiple field elements and combine (concantinate) them in another field. Then, when you build the sumif statement, use the combined elements as the criteria.
Rob