In order to resolve the difficulties involved in inference from a sample of categorical data obtained by using a fallible classifying mechanism (usually inexpensive), we consider, as in Tenenbein (1970, 1971, 1972), the utilization of an additional sample. The second sample is subjected to a simultaneous cross-classification of its elements by the fallible mechanism and by some true (usually expensive) classifying mechanism. The setup is general; i.e., the discussion can be applied to any multidimensional cross-classified data obtained by unrestricted random sampling. Two methodologies are presented: (i) a combined maximum likelihood (ML) and least squares (LS) approach and (ii) a complete-LS approach. Both methodologies are illustrated using real data.