training one SVM model for predicting more than one response variable
e1071 is a highly popular and therefore safe solution for this purpose. 

But if data starts to get bigger I would go with classyfire. It's a quite fresh package built on e1071. It is highly optimized and have some other nice feature too. In my experience it produced similar results to e1071 but with a much faster speed as it was able to utilize all 4 core of my processor.