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Using data samples collected with the BESIII detector at the BEPCII collider at six center-of-mass energies between 4.008 and 4.600 GeV, we observe the processes e+e− → φφω and e+e− → φφφ. The Born cross sections are measured and the ratio of the cross sections σ(e+e− → φφω)/σ(e+e− → φφφ) is estimated to be 1.75 ± 0.22 ± 0.19 averaged over six energy points, where the first uncertainty is statistical and the second is systematic. The results represent first measurements of these interactions.