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Study of the reactions $e^+e^-\to K^+K^-π^0π^0π^0$, $e^+e^-\to K^{0}_{S}K^{\pm}π^{\mp}π^0π^0$, and $e^+e^-\to K^{0}_{S}K^{\pm}π^{\mp}π^+π^-$ at center-of-mass energies from threshold to 4.5 GeV using ISR

We study the processes $e^+e^-\to K^+K^-π^0π^0π^0γ$, $K^{0}_{S}K^{\pm}π^{\mp}π^0π^0γ$, and $K^{0}_{S}K^{\pm}π^{\mp}π^+π^-γ$ 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\invfb. The invariant mass of the hadronic final state defines the effective \epem 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 $e^+e^-\to K^+K^-π^0π^0π^0$, $e^+e^-\to K^0_SK^{\pm}π^{\mp}π^0π^0$, and $e^+e^-\to K^0_SK^{\pm}π^{\mp}π^+π^-$ 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.