A search is reported for near-threshold structures in the J=ψJ=ψ invariant mass spectrum produced in proton-proton collisions at √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 local 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