We have previously applied several models of high-frequency quasi-periodic oscillations ( HF QPOs ) to estimate the spin of the central Kerr black hole in the three Galactic microquasars , GRS 1915+105 , GRO J1655-40 , and XTE J1550-564 .
Here we explore the alternative possibility that the central compact body is a super-spinning object ( or a naked singularity ) with the external space-time described by Kerr geometry with a dimensionless spin parameter a \equiv cJ / GM ^ { 2 } > 1 .
We calculate the relevant spin intervals for a subset of HF QPO models considered in the previous study .
Our analysis indicates that for all but one of the considered models there exists at least one interval of a > 1 that is compatible with constraints given by the ranges of the central compact object mass independently estimated for the three sources .
For most of the models , the inferred values of a are several times higher than the extreme Kerr black hole value a = 1 .
These values may be too high since the spin of superspinars is often assumed to rapidly decrease due to accretion when a \gg 1 .
In this context , we conclude that only the epicyclic and the Keplerian resonance model provides estimates that are compatible with the expectation of just a small deviation from a = 1 .