Kleene star closure of a context free grammar
There is a silly problem that you might need to add a production of the form $S\to\epsilon$, since otherwise you don't necessarily generate $\epsilon$. But the real problem is that $S$ can be used in the right-hand side of productions, and when you add the rule $S\to SS$, things could break. The "correct" way to turn a grammar of $A$ into a grammar of $A^*$ is to add a new start symbol $S'$ and the productions $S' \to S'S|\epsilon$.

In order to find a counterexample, think of the problems mentioned in the previous paragraphs, and try to find an example which manifests them. All it requires is some experimentation.