A dozen X-ray supernova shock breakout (SN SBO) candidates were reported recently based on XMM-Newton archival data, which increased the X-ray-selected SN SBO sample by an order of magnitude. Assuming that they are genuine SN SBOs, we study the luminosity function (LF) by improving on the method used in our previous work. The light curves and the spectra of the candidates were used to derive the maximum volume within which these objects could be detected with XMM-Newton by simulation. The results show that the SN SBO LF can be described by either a broken power law (BPL) with indices (at the 68% confidence level) of 0.48 +/- 0.28 and 2.11 +/- 1.27 before and after the break luminosity at log(L-b/erg s(-1)) = 45.32 +/- 0.55 or a single power law (SPL) with an index of 0.80 +/- 0.16. The local event rate densities of SN SBOs above 5 x 10(42) erg s (-1) are consistent for two models, i.e., 4.6(-1.3)(+1.7) x 10(4) Gpc(-3) yr(-1) and 4.9(-1.4)(+1.9 )x 10(4) Gpc(-3) yr(-1) for BPL and SPL models, respectively. The number of fast X-ray transients of SN SBO origin can be significantly increased by wide-field X-ray telescopes such as the Einstein Probe.