We present a general multi-channel source separation framework where additional audio references are available for one (or more) source(s) of a given mixture.Each audio reference is another mixture which is supposed to contain at least one source similar to one of the target sources.Deformations between the sources of interest and their references are modeled in a linear manner using a generic formulation.This is done by adding transformation matrices to an excitation-filter model, hence affecting different axes, namely frequency, dictionary component or time. A nonnegative matrix co-factorization algorithm and a generalized expectation-maximization algorithm are used to estimate the parameters of the model.Different model parameterizations and different combinations of algorithms are tested on music plus voice mixtures guided by music and/or voice references and on professionally-produced music recordings guided by cover references.Our algorithms improve the signal-to-distortion ratio (SDR) of the sources with the lowest intensity by 9 to 15 decibels (dB) with respect to original mixtures.