If an MMR study uses quantitative methods that are designed to be adequate for a stand alone study, then you should use traditional quantitative standards for evaluating it. Such studies are sometimes referred to as "big quantitative" or QUAN. MMR studies that use "small quan" are actually quite rare.

If there aren't tools already listed via EQUATOR Network you could contact their director for advice on what tool might be relevant https://www.equator-network.org

I agree with David Morgan. All quantitative studies, regardless of type of study, should be evaluated by the diagnostics, sample, and practical effects. There is no difference by what was done before or after.