The isolated neutron star (INS) 2XMM J104608.7-594306 is one of the only two to be discovered through their thermal emission since the ROSAT era. In a first dedicated XMM-Newton observation of the source, we found intriguing evidence of a very fast spin period. We re-observed 2XMM J104608.7-594306 with XMM-Newton to better characterise the spectral energy distribution of the source, confirm the candidate spin period, and possibly constrain the pulsar spin-down. Statistically acceptable spectral fits and meaningful physical parameters for the source are only obtained when the purely thermal spectrum is modified by at least one line in absorption. The implied distance is consistent with a location in (or in front of) the Carina nebula, and radiation radii are compatible with emission originating on most of the surface. Non-thermal X-ray emission is ruled out at levels above 0.5% of the source luminosity. Unfortunately, the second XMM-Newton observation proved inconclusive in terms of confirming (discarding) the fast candidate spin, providing an upper limit on the pulsed fraction of the source that is very close to the limiting sensitivity for detecting the modulation found previously. In the absence of an unambiguous period determination and an estimate of the magnetic field, the nature of the source remains open to interpretation. Its likely association with the Carina cluster and its overall spectral properties (only shared by a handful of other peculiar INSs) disfavour a standard evolutionary path, or one in which the source was previously recycled by accretion in a binary system. The INS 2XMM J104608.7-594306 may be similar to Calvera (1RXS J141256.0+792204), a neutron star for which the scenario of an evolved `anti-magnetar has been discussed. A better age estimate and deeper radio and gamma-ray limits are required to further constrain the evolutionary state of the neutron star.
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