This paper presents our multilingual dependency parsing system as used in the IWPT 2021 Shared Task on Parsing into Enhanced Universal Dependencies. Our system consists of an unfactorized biaffine classifier that operates directly on fine-tuned XLM-R embeddings and generates enhanced UD graphs by predicting the best dependency label (or absence of a dependency) for each pair of tokens. To avoid sparsity issues resulting from lexicalized dependency labels, we replace lexical items in relations with placeholders at training and prediction time, later retrieving them from the parse via a hybrid rule-based/machine-learning system. In addition, we utilize model ensembling at prediction time. Our system achieves high parsing accuracy on the blind test data, ranking 3rd out of 9 with an average ELAS F1 score of 86.97.