@Anna2014, your son is a very strong applicant, especially since you don’t need financial aid. I’m not sure he needs to do ANYTHING to bolster his chances. Just make sure he applies to a variety of schools: not JUST the Ivy Leagues, MIT, Stanford, etc. Those are difficult to get into for any international student whether or not he needs financial aid.
To make sure he gets in somewhere, have your son apply to the top public universities where his full-pay international tuition actually gives him an advantage: schools such as University of California, Berkeley, UCLA, University of Virginia, University of North Carolina, University of Michigan.
Also apply to excellent privates that aren’t Ivies: Caltech, Harvey Mudd, Northwestern etc.