In general the continuation from integer $n$ to $n\to 1$ is a subtle question. For the multientropy, [12] points out that the assumption that the dominant bulk saddle is replica symmetric fails for $n=3$ in the ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ case. Further discussion of replica symmetry for bulk saddles in the ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ case is given in [13]. The situation is similar to that in [43], where a phase transition in the ordinary Rényi entropy was found as a function of $n$. Consequently, the Rényi entropy need not be analytic for all $n$, but only in a neighborhood of $n=1$. Given that a family of replica-symmetric saddles exists for all $n$ and is dominant at sufficiently small $n$ (namely, $n=2$), it is reasonable to similarly conjecture that the replica-symmetric saddles here determine the behavior in the $n\to 1$ limit, although a formal proof would be challenging.