If you start off by measuring the emission spectrum of a grey object and a white object. They will have some common features but some of them are stronger in the white object then the gray and some are the same. By subtracting the features which are stronger with the white from the gray we get to a theoretical black body. It is not as simple but this is the basic concept behind measuring impossible theoretical pure objects. In reality you would have to measure the emission spectrum of thousands of different objects made of various different materials at different temperatures before you know exactly which features is due to the black body radiation and which are from other sources.
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