There is no legal definition of "multi-coating". Minolta was the first Japanese lens maker to apply it -- on ONE glass surface to a lens in 1958. It had two layers of magnesium fluoride -- one thin, one thick. One on top of the other. MULTI-COATING. They are both the same color so there is no way to tell that it is multi-coated. The other lens surfaces were single coated.
Some lenses, just like that early Minolta, but some modern day lenses, even Zeiss lenses, have multi-coating on just one lens element -- and call themselves "multi-coated".
So don't freak out. Some lenses don't look multi-coated, but are, and vice-versa. Minolta, and perhaps some other lens makers, clearly stated that they only use "Achromatic coatings" (their term for multi-coating) if and where it makes a difference. Lots of times it doesn't.
Don't confuse single-colored with single-coated -- or multi-colored with multi-coated. A lens that has a single color might have multi-coatings -- one layer on top of another. Likewise, a lens that has multiple colors might have single-coatings -- on different elements.
Does "multi-coating" mean multiple coatings on the same element? Or does it mean different coatings on different elements? Like I said There is no legal definition of "multi-coating".