Semigroup Isomorphism/Examples/Structure with Two Operations

Examples of Semigroup Isomorphisms
Let $\struct {S_1, \circ_1, *_1}$ and $\struct {S_2, \circ_2, *_2}$ be algebraic structures such that:
 * $\struct {S_1, \circ_1}$ is isomorphic to $\struct {S_1, \circ_2}$
 * $\struct {S_1, *_1}$ is isomorphic to $\struct {S_1, *_2}$

Then it is not necessarily the case that $\struct {S_1, \circ_1, *_1}$ is isomorphic to $\struct {S_2, \circ_2, *_2}$.