We study the processes e+e-→K+K-π0π0π0γ, KS0K±π?π0π0γ, and KS0K±π?π+π-γ in which an energetic photon is radiated from the initial state. The data were collected with the BABAR detector at the SLAC National Accelerator Laboratory. About 1200, 2600, and 6000 events, respectively, are selected from a data sample corresponding to an integrated luminosity of 469 fb-1. The invariant mass of the hadronic final state defines the effective e+e- center-of-mass energy. The center-of-mass energies range from threshold to 4.5 GeV. From the mass spectra, the first ever measurements of the e+e-→K+K-π0π0π0, e+e-→KS0K±π?π0π0, and e+e-→KS0K±π?π+π- cross sections are performed. The contributions from the intermediate states that include η, φ, ρ, K∗(892), and other resonances are presented. We observe the J/ψ and ψ(2S) in most of these final states and measure the corresponding branching fractions, many of them for the first time.