Artificial neural networks (ANN) have revolutionized the field of machine learning by providing impressive human-like performance in solving real-world tasks in computer vision, speech recognition, or complex strategic games. There is a significant interest in developing non-von Neumann coprocessors for the training of ANNs, where resistive memory devices serve as synaptic elements. However, interdevice variability, limited dynamic range and resolution, nonlinearity and asymmetric switching characteristics pose important technical challenges. We investigate the use of multi-memristive synapses to overcome these challenges. We present a detailed experimental characterization of conductance changes using a phase-change memory chip fabricated in the 90nm technology node and show how multi-memrisive synapses can address the limitations of memristive devices for synaptic implementations. Simulations show that an ANN trained with backpropagation can achieve competitive classification accuracies using such a scheme.