We describe a two-stage optimization of the MaltParser system for the ten languages in the multilingual track of the CoNLL 2007 shared task on dependency parsing. The first stage consists in tuning a single-parser system for each language by optimizing parameters of the parsing algorithm, the feature model, and the learning algorithm. The second stage consists in building an ensemble system that combines six different parsing strategies, extrapolating from the optimal parameters settings for each language. When evaluated on the official test sets, the ensemble system significantly outperforms the single-parser system and achieves the highest average labeled attachment score.