This paper reports measurements of processes: e + e − → γK− → γφη and e + e − → γφπ 0 . The initial state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to ≈ 4.6 GeV. The overall size of the data sample analyzed is 232 fb −1 , collected by the BABAR detector running at the PEP-II e + e − storage ring. From the Dalitz plot analysis of the K 0 S K ± π ∓ final state, moduli and relative phase of the isoscalar and the isovector components of the e + e − → KK * (892) cross section are determined. Parameters of φ and ρ recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli and phases of theThe cross section for the OZI-forbidden process e + e − → φπ 0 , and the J/ψ branching fractions to KK * (892) and K + K − η are also measured.