I think it’s important to make a distinction between keeping three major options in play, early on, and being intent on completing all three majors. There’s little benefit to a triple degree. If he’s continuing to grad school, he’ll have to pick one discipline for that; and if he’s going into the workforce, employers will care more about skill-sets and knowledge base than about stacking up majors, so a minor in a secondary field can be more than adequate.
For double (or triple) majors, there doesn’t have to be a common theme - the only potential issue is that some dual majors (where you’re getting a single degree with two majors, rather than two separate degrees) may require a single thesis or capstone that is relevant to both.
My suggestion would be to map out the curriculum for the triple major, but to go in with the intention of paring down to a double major, or a single major with two minors, as he gets farther along and gains clarity about his priorities. If he doesn’t plan to do this, the depth with which he can pursue his primary field (the one he plans to pursue in grad school) will suffer. He simply won’t have as much time for advanced coursework and research as a single-major student who isn’t spreading himself so thin. Strategizing to keep options open is wonderful, but at some point the time will come to make a primary commitment and pare the others back.