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Motivated by the search for type-II multiferroics, we present a comprehensive optical study of a complex oxide family of type-II multiferroic candidates: RbFe(MoO4)2, RbFe(SeO4)2, and RbFe(SO4)2. We employ rotational-anisotropy second harmonic generation spectroscopy (RA SHG), a technique sensitive to point symmetries, to address discrepancies in literature-assigned point/space groups and to identify the correct crystal structures. At room temperature we find that our RA SHG patterns rotate away from the crystal axes in RbFe(AO4)2 (A = Se, S), which identifies the lack of mirror symmetry and in-plane two-fold rotational symmetry. Also, the SHG efficiency of RbFe(SeO4)2 is two orders of magnitude stronger than RbFe(AO4)2 (A = Mo, S), which suggests broken inversion symmetry. Additionally, we present temperature-dependent linear optical characterizations near the band edge of this family of materials using ultraviolet-visible (UV-VIS) absorption spectroscopy. Included is experimental evidence of the band gap energy and band gap transition type for this family. Previously unreported sub-band gap absorption is also presented, which reveals prominent optical transitions, some with an unusual central energy temperature dependence. Furthermore, we find that by substituting the A-site in RbFe(AO4)2 (A = Mo, Se, S), the aforementioned transitions are spectrally tunable. Finally, we discuss the potential origin and impact of these tunable transitions.