Rules regarding Chomsky Normal Form (CNF) grammars
The production

$$S_0 \to S$$

is not in CNF. CNF requires that nonterminals produce either two nonterminals or one terminal. Since the above line shows a nonterminal producing a single nonterminal, it does not fit. The CFG in CNF would be just:

$$S_0 \to XX$$
$$S_0 \to XZ$$
$$\vdots$$

To answer your original questions, though, yes, you can do the above in CNF. There are no stipulations about how many times a nonterminal may appear on the left or whether it can be duplicated on the right.