You say, J, "if there was only one other", but what about two others or five, if we were looking at a situation involving, say, millions of similar things? Where do you stop and why make it at one?
The problem is that, strictly speaking, uniqueness is an absolute quality. In that vein - as I said above - one can be no more 'almost unique' than one can be 'almost a virgin'.
Of course, in language, "usage is king"...if most people accept a way of employing words is acceptable, then acceptable it is and there's an end of the matter. Personally, however, I would never say 'almost unique', as it is not yet acceptable to me.