We use observations of 66 reverberation-measured Mg ii quasars (QSOs) in the redshift range 0.36 ≤ z ≤ 1.686 — a subset of the 78 QSOs we previously studied that also have ${\cal R}_{\rm {Fe\small {II}}}$ (flux ratio parameter of UV Fe ii to Mg ii that is used as an accretion-rate proxy) measurements — to simultaneously constrain cosmological model parameters and QSO 2-parameter and 3-parameter radius-luminosity (R − L) relation parameters in six different cosmological models. We find that these QSO R − L relation parameters are independent of the assumed cosmological model and so these QSOs are standardizable through the R − L relations. Also: (1) With the 2-parameter R − L relation, we find that the low-${\cal R}_{\rm {Fe\small {II}}}$ and high-${\cal R}_{\rm {Fe\small {II}}}$ data subsets obey the same R − L relation within the error bars. (2) Extending the 2-parameter R − L relation to a 3-parameter one does not result in the hoped-for reduction in the intrinsic dispersion of the R − L relation. (3) Neither of the 3-parameter R − L relations provide a significantly better fit to the measurements than does the 2-parameter R − L relation. These are promising results for the on-going development of Mg ii cosmological probes. The first and third of these results differ significantly from those we found elsewhere from analyses of reverberation-measured hβ QSOs.