Experimental findings by CMS on properties of jets and underlying events at high multiplicities in proton–proton interactions at 7 TeV are interpreted as an indication of increasing role of central collisions with small impact parameters. The value of the average impact parameter of the pp collisions as a function of the soft hadron multiplicity is estimated. We find an indication that the rates of different hard processes observed by CMS and ALICE universally depend on the underlying event charged-particle multiplicity until it becomes four times higher than average. It is shown that the increase of the overlap area of colliding protons is not sufficient to explain the rate of jet production in events with charged-particle multiplicity that is more than three times higher than average. New mechanisms are necessary, like interaction of protons in rare configurations of higher than average gluon density. Such mechanisms are not included in the present Monte Carlo event generators. Further studies are proposed.