  In this paper it is shown that the lattice of C$^*$-covers of an operator
algebra does not contain enough information to distinguish operator algebras up
to completely isometric isomorphism. In addition, four natural equivalences of
the lattice of C$^*$-covers are developed and proven to be distinct. The
lattice of C$^*$-covers of direct sums and tensor products are studied. Along
the way key examples are found of an operator algebra that generates exactly
$n$ C$^*$-algebras up to $*$-isomorphism and a simple operator algebra that is
not similar to a C$^*$-algebra.
