And yes, sets in general cannot contain duplicates. I’m not intimately familiar with the Java libraries, so I’m not sure what class would suit you better.
If you’re looking for a tree map that can have multiple objects for one key, check out Google’s TreeMultimap at http://guava-libraries.googlecode.com/svn/trunk/javadoc/index.html . However, you can still only have one key-value pair (but you can store multiple values for the same key).