A difficult question to answer. Stirnert and Wolcott differ on the lineage itself, but both cite Visitation of Shropshire as a source for the Bramptons. Wolcott's citation adds: "SOURCES:
[1] Visitation of Shropshire of 1623, pp 304 for the chart down to the marriages of the two Brampton ladies c. 1300. That pedigree contains much anachronistic data which we have emended to follow a realistic timeline". Neither man designates on Bryn from the other via a suffix.
Not saying it's true in this case, but I would caution against assuming that the ordinal suffixes applied to a family in a straight line. You will find that grandfather may have been named Steve. He had two sons, one named Steve, the other Heathcliff. Then Heathcliff had a son named Steve. So, on face value, many people would think that Steve, the grandson of the first Steve, should be Steve II, when actually it is his uncle that is Steve II, etc.