  We study electron transport through a multi-level quantum dot with Rashba
spin-orbit interaction in the presence of local Coulomb repulsion. Motivated by
recent experiments, we compute the level splitting induced by the spin-orbit
interaction at finite Zeeman fields $B$, which provides a measure of the
renormalized spin-orbit energy. This level splitting is responsible for the
suppression of the Kondo ridges at finite $B$ characteristic for the
multi-level structure. In addition, the dependence of renormalized $g$-factors
on the relative orientation of the applied $B$ field and the spin-orbit
direction following two different protocols used in experiments is
investigated.
