  The KLEVER experiment aims to measure ${\rm BR}(K_L \to \pi^0 \nu
\overline{\nu})$, supplementing the ongoing NA62 measurement of ${\rm BR}(K^+
\to \pi^+ \nu \overline{\nu})$, to provide new input on CKM unitarity and
potentially new physics. KLEVER is undergoing continuous development, with
particular efforts focused on the design of the target and the beamline. As
described here, adaptations are required relative to the K12 beamline in its
current format, and a series of simulations has been performed to ensure that
an adequate particle flux can be achieved while simultaneously suppressing
problematic backgrounds.
