On function "plot_partial_dependence", I think the "target" parameter is being ignored (in the multiclass setting) since the following line:

sets target_idx to 0 every time (ignoring previous lines in which the right column is selected).

When I run:

plot_partial_dependence(rf, X, [feature_column], feature_names=X.columns,  target="class_1", response_method="predict_proba", n_jobs=-1) 
plot_partial_dependence(rf, X, [feature_column], feature_names=X.columns,  target="class_2", response_method="predict_proba", n_jobs=-1) 

I get the same result two times (and I believe that result to be the "class_1" result)