  We present magnetoresistance studies of the quasi-two-dimensional organic
conductor $\kappa$-(BETS)$_2$Mn[N(CN)$_2$]$_3$, where BETS stands for
bis\-(ethylene\-dithio)\-tetra\-selena\-fulvalene. Under a moderate pressure of
1.4\,kbar, required for stabilizing the metallic ground state, Shubnikov - de
Haas oscillations, associated with a classical and a magnetic-breakdown
cyclotron orbits on the cylindrical Fermi surface, have been found at fields
above 10\,T. The effective cyclotron masses evaluated from the temperature
dependence of the oscillation amplitudes reveal strong renormalization due to
many-body interactions. The analysis of the relative strength of the
oscillations corresponding to the different orbits and its dependence on
magnetic field suggests an enhanced role of electron-electron interactions on
flat parts of the Fermi surface.
