I recal reading a very long thread on filters. The question was not realy about "multicoated" filters so much as "multiple" filters.
(Or at least that's the way I took it).
One person (the first poster?) showed sise by side photos of the same subject taken with the same camera with the same lens.
The difference was one was taken with no filter and the other was taken with dozens of filters all on the lens at the same time!
It proved that any filters can degrade your photo by the fact you have introduced another layer of glass that may have some light bounced from the surface of your lens to the filter then some of that light reflected back into the lens.
He proved his point with the dozens of filters all on the lens an one time but how much is the degradation with a single... or for that mater, a few filters cause. Most of us would not notice in side to side comparisons. Otherwise we would remove our UV filter to put on our polarizer and may never use a filter with a progressive color to enhance a blue sky or a red sunset.
Cokin P filters anyone?