  A search is reported for near-threshold structures in the J/$\psi$J/$\psi$
invariant mass spectrum produced in proton-proton collisions at $\sqrt{s}$ = 13
TeV from data collected by the CMS experiment, corresponding to an integrated
luminosity of 135 fb$^{-1}$. Three structures are found, and a model with
quantum interference among these structures provides a good description of the
data. A new structure is observed with a significance above 5 standard
deviations at a mass of 6638 $^{+43}_{-38}$ (stat) $^{+16}_{-31}$ (syst) MeV.
Another structure with even higher significance is found at a mass of 6847
$^{+44}_{-28}$ (stat) $^{+48}_{-20}$ (syst) MeV, which is consistent with the
X(6900) resonance reported by the LHCb experiment and confirmed by the ATLAS
experiment. Evidence for another new structure, with a local significance of
4.7 standard deviations, is found at a mass of 7134 $^{+48}_{-25}$ (stat)
$^{+41}_{-15}$ (syst) MeV. Results are also reported for a model without
interference, which does not fit the data as well and shows mass shifts up to
150 MeV relative to the model with interference.
