  We continue the search for rules that govern when off-shell 4D, $\cal N$ = 1
supermultiplets can be combined to form off-shell 4D, $\cal N$ = 2
supermultiplets. We study the ${\mathbb S}_8$ permutations and Height Yielding
Matrix Numbers (HYMN) embedded within the adinkras that correspond to these
putative 4D, $\cal N$ = 2 supermultiplets off-shell supermultiplets. Even
though the HYMN definition was designed to distinguish between the raising and
lowering of nodes in one dimensional valises supermultiplets, they are shown to
accurately select out which combinations of off-shell 4D, $\cal N$ = 1
supermultiplets correspond to off-shell 4D, $\cal N$ = 2 supermultiplets. Only
the combinations of the chiral + vector and chiral + tensor are found to have
valises in the same class. This is consistent with the well known structure of
4D, $\cal N$ = 2 supermultiplets.
