In this paper we introduce the notion of  a super
commutative $d$-algebra and we show that if $(X;*)$ is a
commutative binary system, then by adjoining an element $0$ and
adjusting the multiplication  to $x*x = 0$, we obtain a super
commutative  $d$-algebra, thereby demonstrating that the class of
such algebras is very large. We also note that the class of super
commutative $d$-algebras is Smarandache disjoint from the class
of $BCK$-algebras, once more indicating that the class of
$d$-algebras is quite a bit larger than the class of
$BCK$-algeras and  leaving the problem of finding further classes of
$d$-algebras of special types which are Smarandache disjoint from
the classes of $BCK$-algebras and super commutative $d$-algebras
as an open question.  Lastly the idea of a super Smarandache
class of algebras is also defined and investigated.