In recent years, much work has been done in Statistics on the estimation of network structure. Network structure can be defined in many ways, such as by sparse covariance matrices (encoding marginal associations), precision matrices (describing conditional associations) or by correlation matrices. Considerable work has been done in all of these settings for the estimation of the structure of a single network, and estimating the structure of multiple, related networks has been well studied in the sparse covariance and precision matrix settings. Estimating the structure of multiple related networks defined by correlation matrices is an area which has remained relatively unexplored, and this is where we focus our efforts. The correlation matrix yields a more flexible network setting, where the gaussianity assumption can be relaxed, but it cannot be neatly translated into a graphical model in the way that networks arising from covariance or precision matrices can. Inspired by lipidomics data from a control feeding experiment on humans, we develop a factor analysis approach to estimating the structure of related correlation matrices. We present the theoretical framework for two different formulations of the model, anchoring the models in a biological context. Algorithms for both formulations are presented, as well as a thorough performance review for one of the algorithms. We conclude with an overview of our next steps, plus a brief mention of some of the datasets we have available to us, which are suitable for our method.