There doesn't seem to be any reason why Beauchamp-109 can't be called William IV.
This is the traditional version, as given by Genealogics
http://www.genealogics.org/descendtext.php?personID=I00174742&tree=LEO&display=block&generations=6
MedLands gives a different version
http://fmg.ac/Projects/MedLands/ENGLISHNOBILITYMEDIEVAL3.htm#WilliamBeauchampdied1170
According to this, William I married Bertha not Maud de Braose, William II married Amice Unknown not Joan, and Walter was the brother not the son of William III (who died underage and unmarried). Keats-Rohan is cited. It's mentioned that Bertha is incorrectly placed by an IPM, which might account for the confusion. It admits the chronology is not ideal.
We give William II a son Andrew, who existed but doesn't seem to belong to this family at all. Not all Beauchamps were related.
