When recording a live musical performance, the different voices, such as the instrument groups or soloists of an orchestra, are typically recorded in the same room simultaneously, with at least one microphone assigned to each voice. However, it is difficult to acoustically shield the microphones. In practice, each one contains interference from every other voice. In this paper, we aim to reduce these interferences in multi-channel recordings to recover only the isolated voices. Following the recently proposed Kernel Additive Modeling framework, we present a method that iteratively estimates both the power spectral density of each voice and the corresponding strength in each microphone signal. With this information, we build an optimal Wiener filter, strongly reducing interferences. The trade-off between distortion and separation can be controlled by the user through the number of iterations of the algorithm. Furthermore, we present a computationally effective approximation of the iterative procedure. Listening tests demonstrate the effectiveness of the method.