Does "rare steak" have any other meaning than its seeming meaning as not very well cooked meat?
It's unlikely. e. a type of steak that is not widely available, but since the "lightly cooked" meaning is so common and familiar, it doesn't seem very helpful to use it in that way.
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It's unlikely. Of course, in theory it could mean "unusual steak", i.e. a type of steak that is not widely available, but since the "lightly cooked" meaning is so common and familiar, it doesn't seem very helpful to use it in that way. More context is needed in order to be sure.