Multispectral imaging is a technique that captures data across several bands of the light spectrum, and it can be useful in many computer vision fields, including color constancy. We propose a method that exploits multispectral imaging for illuminant estimation, and then applies illuminant correction in the raw RGB domain to achieve computational color constancy. Our proposed method is composed of two steps: first, a selected number of existing camera-independent algorithms for illuminant estimation, originally designed for RGB data, are applied in generalized form to work with multispectral data. We demonstrate that the sole multispectral extension of such algorithms is not sufficient to achieve color constancy, and thus we introduce a second step, in which we re-elaborate the multispectral estimations before conversion into raw RGB with the use of the camera response function. Our results on the NUS dataset show that an improvement of 60% in the color constancy performance, measured in terms of reproduction angular error, can be obtained according to our method when compared to the traditional raw RGB pipeline.