Yes, you can accomplish your sort without creating a new comparator.
There is a well-known trick for sorting by a primary field, secondary, tertiary, etc: First sort by the least important field (tertiary), then the next important field (secondary), and finally the most important field (primary). But the sorting algorithm needs to be stable for this to work.
If you are sorting an array, use Arrays.sort(). If you are sorting a List, use Collections.sort(). Both of these methods are guaranteed to be stable.
Suppose your primary comparator object is stored in the variable primaryComp, and your secondary is in secondaryComp. Then here is some code to accomplish what you want:
Arrays.sort(mylist, secondaryComp); // This must come first!
Arrays.sort(mylist, primaryComp);