We explore the task of multi-source morphological reinflection, which generalizes the standard, single-source version. The input consists of (i) a target tag and (ii) multiple pairs of source form and source tag for a lemma. The motivation is that it is beneficial to have access to more than one source form since different source forms can provide complementary information, e.g., different stems. We further present a novel extension to the encoder-decoder recurrent neural architecture, consisting of multiple encoders, to better solve the task. We show that our new architecture outperforms single-source reinflection models and publish our dataset for multi-source morphological reinflection to facilitate future research.