For example, admission to a benefit concert may be afforded by a suggested minimum donation. Or perhaps by a minimum suggested donation. To me, the latter feels not quite right, like the minimum qualifier is being applied to the wrong place.
In fact, I think that adding minimum and suggested should be mutually exclusive here. Either the donation is a suggested amount, or it has a specified minimum. I can see, though, that the intention is to not place a hard limit on the entry fee, otherwise it's not really more than a ticket price. And at the same time, they want to encourage donations that are more than the minimum.
So, given that both adjectives are applied, is there a semantic difference when you switch the order?