Is natural isomorphism unique？

suppose $F,G\in Ob(Fct(\mathscr C_1,\mathscr C_2))$ are functors,and $\theta:F\Leftrightarrow G$ is an natural isomorphism between $F$ and $G$

my question is : Are there any other $\theta':F\Leftrightarrow G$ is also an natural isomorphism between $F$ and $G$ but different from $\theta$ ? Meaning exist $X\in Ob(\mathscr C_1)$, s.t. $\theta_X$ is different from $\theta'_X$

In general, there can be many, just as there can be many bijections from a set to itself or many automorphisms of an algebraic object. Actually, this allows you to easily construct concretecounterexamples if you choose your categories in a smart way.