The bar set for this project is a high one:  to test at least two patrilineal line male descendants of every ROSE family in the world!  That way, and from then on, any ROSE male can be Y-DNA tested and immediately know where his ROSE origin lies.

I say "at least" two descendants because if two are tested and they don't match, it means at least one of them has an NPE.  And I say "at least" one has an NPE because I once had a family where the first three men tested did not match each other.  Only when the fourth man was tested did one of them get a match — and, yes, the paper genealogy of all four was well documented.  It is for that reason, by the way, that every man interested in proving his biological origin needs to be Y-DNA tested.  It doesn't matter how correct and documented your paper genealogy is, you cannot know whether or not you have an NPE unless you are Y-DNA tested.  The NPE rate in my projects is running about 10%.

If you are a ROSE who has been tested, and you find you have no match, the way to increase the odds of getting one is to encourage other ROSE males to be tested, especially ones whose claim the same ROSE progenitor you do.