DJ mix transcription is a crucial step towards DJ mix reverse engineering, which estimates the set of parameters and audio effects applied to a set of existing tracks to produce a performative DJ mix. We introduce a new approach based on a multi-pass NMF algorithm where the dictionary matrix corresponds to a set of spectrogram slices of the source tracks present in the mix. The multi-pass strategy is motivated by the high computational cost resulting from the use of a large NMF dictionary. The proposed method uses inter-pass filtering to favor temporal continuity and sparseness and is evaluated on a publicly available dataset. Our comparative results considering a baseline method based on dynamic time warping (DTW) are promising and pave the way of future NMF-based applications.