If the columns are included in the existing index, the existing index is a covering set. It is possible that the optimizer will use the existing index via skip scan, but it also depends on the cardinality of the columns (e.g., fewer values up front, more values towards the end). How do the existing and proposed indexes compare in terms of leading columns? For example, if the first three of the existing match the order of the proposed, it's a no-brainer (waste of time to create the new index). If the proposed happens to be the last three columns of the existing, that is more likely to be a better candidate for a new index. If they are interspersed, test and see.

In 11g, you can use invisible indexes within a session and see right then and there which is better. If you like the results, mark the index as visible.