  We search for transient sources in a sample of ULXs from the 3XMM-DR4 release
of the XMM-Newton Serendipitous Source Catalogue in order to find candidate
neutron star ULXs alternating between an accreting state and the propeller
regime, in which the luminosity drops dramatically. By examining their fluxes
and flux upper limits, we identify five ULXs that demonstrate long-term
variability of over an order of magnitude. Using Chandra and Swift data to
further characterise their light curves, we find that two of these sources are
detected only once and could be X-ray binaries in outburst that only briefly
reach ULX luminosities. Two others are consistent with being super-Eddington
accreting sources with high levels of inter-observation variability. One
source, M51 ULX-4, demonstrates apparent bimodal flux behaviour that could
indicate the propeller regime. It has a hard X-ray spectrum, but no significant
pulsations in its timing data, although with an upper limit of 10% of the
signal pulsed at ~1.5 Hz a pulsating ULX cannot be excluded, particularly if
the pulsations are transient. By simulating XMM-Newton observations of a
population of pulsating ULXs, we predict that there could be approximately 200
other bimodal ULXs that have not been observed sufficiently well by XMM-Newton
to be identified as transient.
