$A$ be a basis for a topology on $X$, and $\tau_X$ be a topology on $X$ s.t $A \subseteq \tau_X$. Then can we complete $A$ to a basis of $\tau_X$?

Question

Let $A$ be a basis for a topology on $X$, and let $\tau_X$ be a topology on $X$ such that $A \subseteq \tau_X$. Then can we complete $A$ to a basis of $\tau_X$ ? (i.e there exists a basis $B$ of $\tau_X$ s.t $A \subseteq B$)

If so, how ? I mean is there any general procedure ? If not, how can we prove that is it always not possible, i.e can you provide a counterexample ?