A search is reported for near-threshold structures in the 𝐽/𝜓⁢𝐽/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.