How do you perform multilabel classification that is also a multiclass problem?
From the description this is not a multilabel problem because:

Each of the three &quot;classes&quot; (columns) must have a label. In a multilabel problem every class is optional.
Every &quot;class&quot; (column) appears to have a specific purpose subdivided into 4 labels. In a regular multilabel problem the labels are exchangeable, e.g. a document can have topics &quot;sports&quot; and &quot;society&quot; but not &quot;politics&quot;, all of these labels have no order and no specific role distinct from the others.

It seems that you simply have three regular independent multiclass problems:

problem 1 = predict &quot;class 1&quot;
problem 2 = predict &quot;class 2&quot;
problem 3 = predict &quot;class 3&quot;

Note: the word &quot;class&quot; for the columns is confusing because these don't correspond to the regular concept of class.