  Fitting the thermal continuum emission of accreting black holes observed
across X-ray bands represents one of the principle means of constraining the
properties (mass and spin) of astrophysical black holes. Recent ''continuum
fitting'' studies of Galactic X-ray binaries in the soft state have found best
fitting dimensionless spin values which run into the prior bounds placed on
traditional models ($a_\star = 0.9999$). It is of critical importance that
these results are robust, and not a result solely of the presence of these
prior bounds and deficiencies in conventional models of accretion. Motivated by
these results we derive and present superkerr, an XSPEC model comprising of a
thin accretion disc solution valid in the Kerr geometry for arbitrary spin
parameter $a_\star$, extending previous models valid only for black holes
($|a_\star| < 1$). This extension into ''superextremal'' spacetimes with
$|a_\star| > 1$ includes solutions which describe discs evolving around naked
singularities, not black holes. While being valid solutions of Einstein's field
equations these naked singularities are not expected to be present in nature.
We discuss how the ''measurement'' of a Kerr spin parameter $1 < a_\star < 5/3$
would present compelling evidence for the requirement of a rethink in either
standard accretion theory, or our theories of gravity.
