Multivariate analysis

No. I don't think so. And I don't think that is what "multivariate" means.

I rather think all of Weka's APIs and classifiers assume that there is exactly one attribute which gets assigned the "class" attribute label (that's the column to be predicted/classified).

Although there is a MultiClassClassifier meta-classifier, this is designed to improve algorithms that can only handle binary class-attribute prediction problems (e.g. Weka's Glass.arff dataset with Logistic regression)

Depending on the number of dependent variables (when they are categorical) you could also consider doing the following. Imagine we have images of cats and dogs which are happy and sad.

We could concatenate the classes into derived classes. E.g. happy cat, sad cat, happy dog, and sad dog. If the classes are not too many for the dependent variable this should work.

An alternative would be to use two classifiers. One for the first class (animal type) and another for the second class (mood). This procedure has the drawback that you need two classifiers. But you could have small and efficient classifiers to do the job. This method is good when there is not a correlation between the different dependent variables. In my example, this would mean that there is no bias in the population that cats/dogs are happier than dogs/cats. If the correlation is larger then the previous approach is better suited because your network can use the correlation to make better decisions.