Since the discovery of SN (supernova) 1987A, the number of Type II-peculiar SNe has grown, revealing a rich diversity in photometric and spectroscopic properties. In this study, using a single 15Msun low-metallicity progenitor that dies as a blue supergiant (BSG), we have generated explosions with a range of energies and 56Ni masses. We then performed the radiative transfer modeling with CMFGEN from 1d until 300d after explosion. Our models yield light curves that rise to optical maximum in ~100d, with a similar brightening rate, and with a peak absolute V-band magnitude spanning from -14 to -16.5mag. All models follow a similar color evolution, entering the recombination phase within a few days of explosion, and reddening further until the nebular phase. Their spectral evolution is analogous, mostly differing in line profile width. With this model set, we study the Type II-pec SNe 1987A, 2000cb, 2006V, 2006au, 2009E, and 2009mw. Their photometric and spectroscopic diversity suggest that there is no prototypical Type II-pec SN. These SNe brighten to maximum faster than our model set, except perhaps SN2009mw. The spectral evolution of SN1987A conflicts with other observations and with model predictions from 20d until maximum: Halpha narrows and weakens while BaII lines strengthen faster than predicted, which we interpret as signatures of clumping. SN2000cb rises to maximum in only 20d and shows weak BaII lines. Its spectral evolution is well matched by an energetic ejecta but the light curve may require asymmetry. The persistent blue color, narrow lines, and weak Halpha absorption, seen in SN2006V conflicts with expectations for a BSG explosion powered by 56Ni and may require an alternative power source. In addition to diversity arising from different BSG progenitors, we surmise that their ejecta are asymmetric, clumped, and, in some cases, not solely powered by 56Ni decay [abridged].
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