Measurement of cross sections of the interactions e⁺e⁻ → ϕϕω and e⁺e⁻ → ϕϕϕ at center-of-mass energies from 4.008 to 4.600 GeV

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.