Small-limit conjecture for presentable n-categories

Let $n\geq 0$. The category $n\operatorname{Pr}^L$ denotes the category of presentable $n$-categories and left adjoint functors.

Small-limit conjecture. The category $n\operatorname{Pr}^L$ has all small limits for all $n\geq 0$.

This is presented as a closure property expected for the world of presentable $n$-categories, extending the corresponding stability properties of presentable $1$-categories. The supplied text gives no resolution of the claim.