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In this paper we discuss the impact of the Double Parton Scattering (DPS)mechanism for the production of $J/\psi$ pairs at the COMPASS energy. We findthat the kinematics suppresses the DPS cross section by a factor of $\sim1/2$.The upper limit for the double $J/\psi$ production DPS cross section at theCOMPASS energy is estimated. The Feynman-$x$ distributions of double $J/\psi$production with the CERN $\pi^-$ beam are presented.

Phenomenological analysis of the possible impact of Double Parton  Scattering in double $J/\psi$ production at the COMPASS detector using the  CERN $\pi^-$ beam at 190 GeV/c