Well I would expect a PPL who gets into a MU-2 to expect to need additional training
And the amount of training would be truly huge compared to the tech knowledge one gets in a plain PPL.
A SEP doesn't need anything beyond a "complex conversion", unless it is one of very few prescribed types. I think a Malibu (?) is one of those, because of pressurisation.
But then you cannot make proper use of such a plane unless you have a full IR, anyway. It's different in the USA (no Class A below 18000ft) where a PPL can fly a jet with just a type rating.