As far as I know, the only way to offer a self-sponsored MPL within the existing regulatory framework would be to attach it to a pay-for-your-own-line-training scheme. I and most others have a pretty low opinion of pay-to-fly and given the widespread skepticism towards MPL, I'd have to rank an SSPTFMPL as a very dodgy thing indeed. By the way, that new acronym means Self Sponsored Pay To Fly MPL.
There is an interesting corollary discussion presently on the Evidence of an Upturn thread regarding experience levels and accidents. A very salient point in that discussion is the fact that MPL brings back rigorous airline selection, while self sponsored training has a large element of self selection in it. Integrated schools have a selection process and some are probably more rigorous than others, but the process used to select cadets is one of the most rigorous and it's a safe bet that any airline venturing into the unproven MNPL will be even more vigilant who they choose for the first few years of MPL. This can only be a good trend and is a hidden benefit of MPL.