  We propose the general scheme of incorporation of the Dirac monopoles into
mechanical systems on the three-dimensional conformal flat space. We found that
any system (without monopoles) admitting the separation of variables in the
elliptic or parabolic coordinates can be extended to the integrable system with
the Dirac monopoles located at the foci of the corresponding coordinate
systems. Particular cases of this class of system are the two-center
MICZ-Kepler system in the Euclidean space, the limiting case when one of the
background dyons is located at the infinity as well as the model of particle in
parabolic quantum dot in the presence of parallel constant uniform electric and
magnetic fields.
