We study the processes e+e--->\u92KS0KLpi0gamma, KS0KL0eta gamma, and KS0KL0pi0pi0gamma, where the photon is radiated from the initial state, providing cross section measurements for the hadronic final states over a continuum of center-of-mass energies. The results are based on 469 fb-1 of data collected at or near the Upsilon(4S) resonance with the BABAR detector at SLAC. We present the first measurements of the e+e--->KS0KL0pi0, KS0KL0eta, and KS0KL0pi0pi0 cross sections up to a center-of-mass energy of 4 GeV and study their intermediate resonance structures. We observe J/psi decays to all of these final states for the first time, present measurements of their J/psi branching fractions, and search for psi(2S) decays
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