> The option I introduced was not to overwrite what was done in fit but for the case that fit is not called btw.

I see. In that case, there are three cases: multiclass, list of lists and indicator matrix. So @arjoly's earlier suggestion to use a string makes sense to me (and will avoid mutually inconsistent combination).

I personally still prefer to have it as parameter of `inverse_transform` if there is no major benefit in having it a constructor parameter. Also note that `inverse_transform` already has a `threshold` option.