  We expand the Cooper problem by including a third electron in an otherwise
empty band. We demonstrate the formation of a trimer state of two electrons
above the Fermi sea and the third electron, for sufficiently strong inter-band
attractive interaction. We show that the critical interaction strength is the
lowest for small Fermi velocities, large masses of the additional electron and
large Debye energy. This trimer state competes with the formation of the
two-electron Cooper pair, and can be created transiently via optical pumping.
