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 fini
te 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.
