To do another Master's, already holding a PhD
Surely you're joking Mr. Feynman!

Sorry, but you walked into that joke. Actually, such an application would occur so infrequently that it might result in a few chuckles. But I don't think it would have a lot of effect. But certainly not a big advantage. 

In fact, people, including myself, will wonder why a person would bother. After all, the applicant can study and learn effectively and evidenced by the doctorate, so what is the need of a formal program. It might be a disadvantage in some places where the available slots are limited and people would feel they should be given to someone who needs the training more. 

On the other hand, if a lab needs particular skills that you have, they might be interested, just for that. 

Thus, it is impossible to say in general as local needs/beliefs will dominate such a situation.