  We study a mesoscopic interacting quantum dot described by the "universal
Hamiltonian" that is coupled to a Kondo spin. The ferromagnetic exchange
interaction within the dot leads to a stepwise increase of the ground state
spin; this Stoner staircase is modified non-trivially by the Kondo interaction.
We find that the spin-transition steps move to lower values of the exchange
coupling for weak Kondo interaction, but shift back up for sufficiently strong
Kondo coupling. The problem is solved numerically by diagonalizing the system
Hamiltonian in a customized good-spin basis and analytically in the weak and
strong Kondo coupling limits. The interplay of Kondo and ferromagnetic exchange
can be probed with experimentally tunable parameters.
