  Double parton scattering (DPS) is studied at the example of $J/\psi$
pair-production in the LHCb and ATLAS experiments of the Large Hadron Collider
(LHC) at centre-of-mass energies of $\sqrt{S}=$ 7, 8, and 13 TeV. We report
theoretical predictions delivered to the LHCb and ATLAS collaborations adjusted
for the fiducial volumes of the corresponding measurements during Run I and
provide new predictions at 13 TeV collision energy. It is shown that DPS can
lead to noticeable contributions in the distributions of longitudinal variables
of the di-$J/\psi$ system, especially at 13 TeV. The increased DPS rate in
double $J/\psi$ production at high energies will open up more possibilities for
the separation of single parton scattering (SPS) and DPS contributions in
future studies.
