Anything's possible, of course, but normally the first, middle, (however many others), and last names match for a Jr.
My father and grandfather were both Herbert Edward (Sr and Jr). My parents kindly gave me a different middle name, so no one would call me Herb the Third. And no one ever did. :)
It seems you have pretty solidly IDed the Philips. If you are absolutely certain about the middle names, I think it calls for a note in Junior's bio.