  We investigate the combined effect of spin-orbit scattering and
electron-electron interactions on the probability distribution of $g$-factors
of metal nanoparticles. Using random matrix theory, we find that even a
relatively small interaction strength %(ratio of exchange constant $J$ and mean
level %spacing $\spacing$ $\simeq 0.3$) significantly increases $g$-factor
fluctuations for not-too-strong spin-orbit scattering (ratio of spin-orbit rate
and single-electron level spacing $1/\tau_{\rm so} \spacing \lesssim 1$), and
leads to the possibility to observe $g$-factors larger than two.
