Genomic selection (GS) reports on milk fatty acid (FA) profiles have been published quite recently and are still few despite this trait represents the most important aspect of milk nutritional and sensory quality. Reasons for this can be found in the high costs of phenotype recording but also in issues related to its nature of complex trait constituted by multiple genetically correlated variables with low heritabilities. One possible strategy to deal with such constraint is represented by the use of dimension reduction methods. We analysed 40 individual FAs from Italian Brown Swiss, Holstein and Simmental milk through multivariate factor analysis (MFA) to study the genetics of milk FA-related latent variables (factors) and assess their potential use in breeding. A total of nine factors were obtained, and their genetic parameters were inferred under a Bayesian framework using two statistical approaches: the classical pedigree best linear unbiased prediction (ABLUP) and the single-step genomic BLUP (ssGBLUP). The resulting factorial solutions were able to represent groups of FAs with common origin and function and can be considered concise pathway-level phenotypes. The heritability (h2 ) values showed relevant variations across different factors in each breed (0.03 ≤ h2  ≤ 0.38). The accuracies of breeding values predicted were low to high, ranging from 0.13 to 0.72 and from 0.18 to 0.74 considering the pedigree and the genomic model, respectively. The gain in accuracy in genetic prediction due to the addition of genomic information was ~30% and ~5% in validation and training groups respectively, confirming the contribution of genomic information in yielding more accurate predictions compared to the traditional ABLUP methodology. Our results suggest that MFA in combination with GS can be a valuable tool in dairy cattle breeding and deserves to be further investigated for use in future breeding programs to improve cow's milk FA-related traits.