  A prime motivation for compiling catalogues of any celestial X-ray source is
to increase our numbers of rare sub-classes. In this work we take a recent
multi-mission catalogue of ultraluminous X-ray sources (ULXs) and look for
hitherto poorly-studied ULX candidates that are luminous ($L_{\rm X} \geq
10^{40} \rm ~erg~s^{-1}$), bright ($f_{\rm X} \geq 5 \times 10^{-13} \rm
~erg~cm~s^{-1}$) and have archival XMM-Newton data. We speculate that this
luminosity regime may be ideal for identifying new pulsating ULXs (PULXs),
given that the majority of known PULXs reach similar high luminosities. We find
three sources that match our criteria, and study them using archival data. We
find 4XMM J165251.5-591503 to possess a bright and variable Galactic optical/IR
counterpart, and so conclude it is very likely to be a foreground interloper.
4XMM J091948.8-121429 does appear an excellent ULX candidate associated with
the dwarf irregular galaxy PGC 26378, but has only one detection to date with
low data quality. The best dataset belongs to 4XMM J112054.3+531040 which we
find to be a moderately variable, spectrally hard ($\Gamma \approx 1.4$) X-ray
source located in a spiral arm of NGC 3631. Its spectral hardness is similar to
known PULXs, but no pulsations are detected by accelerated pulsation searches
in the available data. We discuss whether other missions provide objects for
similar studies, and compare this method to others suggested for identifying
good PULX candidates.
