Measurement of cross sections of the interactions e(+)e(-) -> phi phi omega and e(+)e(-) -> phi phi phi 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(-) -> phi phi omega and e(-)e(-) -> phi phi phi. The Born cross sections are measured and the ratio of the cross sections sigma(e(+)e(-) -> phi phi omega)/sigma(e(-)e(-) -> phi phi phi) 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.