  We study reductions of the Korteweg--de Vries equation corresponding to
stationary equations for symmetries from the noncommutative subalgebra. An
equivalent system of $n$ second-order equations is obtained, which reduces to
the Painlev\'e equation P$_{34}$ for $n=1$. On the singular line $t=0$, a
subclass of special solutions is described by a system of $n-1$ second-order
equations, equivalent to the P$_3$ equation for $n=2$. For these systems, we
obtain the isomonodromic Lax pairs and B\"acklund transformations which form
the group ${\mathbb Z}^n_2\times{\mathbb Z}^n$.
