In Chemometrics, the coupling of different kinds of measurements including genomics, proteomics and metabolomics generates a large amount of variables structured into meaningful blocks for the characterization of the same set of samples. Dealing with multi-blocks data in a discrimination scope, we propose, herein, to extend the PLS method to discrimination (PLS-DA), considering the decomposition of the between groups covariance matrix in the multi-block context. This leads to the simultaneous determination of global and block components. This method is illustrated on a case study pertaining to the LACATOL project (registered to the French Clinical Trial under N° NCT01493063) which aims at ensuring the optimal growth of preterm newborns through a personalized nutrition. A multi-block PLS-DA is performed to identify two phenotypes of milk, associated with a growth group (normal vs slow) of preterm newborns. The relationships between metabolomics, free amino acids and macronutriments are highlighted.