  Three- and four-jet production is measured in deep-inelastic $ep$ scattering
at low $x$ and $Q^2$ with the H1 detector using an integrated luminosity of
$44{.}2 {\rm pb}^{-1}$. Several phase space regions are selected for the
three-jet analysis in order to study the underlying parton dynamics from global
topologies to the more restrictive regions of forward jets close to the proton
direction. The measurements of cross sections for events with at least three
jets are compared to fixed order QCD predictions of ${\mathcal{O}}(\alpha_{\rm
s}^2)$ and ${\mathcal{O}}(\alpha_{\rm s}^3) $ and with Monte Carlo simulation
programs where higher order effects are approximated by parton showers. A good
overall description is provided by the ${\mathcal{O}}(\alpha_{\rm s}^3) $
calculation. Too few events are predicted at the lowest $x \sim 10^{-4}$,
especially for topologies with two forward jets. This hints to large
contributions at low $x$ from initial state radiation of gluons close to the
proton direction and unordered in transverse momentum. The Monte Carlo program
in which gluon radiation is generated by the colour dipole model gives a good
description of both the three- and the four-jet data in absolute normalisation
and shape.
