Can we perform an end-to-end music source separation with a variable number of sources using a deep learning model? We present an extension of the Wave-U-Net model which allows end-to-end monaural source separation with a non-fixed number of sources. Furthermore, we propose multiplicative conditioning with instrument labels at the bottleneck of the Wave-U-Net and show its effect on the separation results. This approach leads to other types of conditioning such as audio-visual source separation and score-informed source separation.