# What is the method used in statistical classification when dealing with multi-dimensional discrete target labels?

If the training set is a set of $n$-tuples, with discrete labels, one can standardly use multinomial logistic regression (softmax), but what if the target labels are pairs of discrete values, or more generally, an $m$-tuple of discrete values?

Is there any method I can use, or am I allowed to perform $m$ separate softmax regression classifications, for each target dimension?

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