You could perform multiple group structural equation modelling where each dataset represents one group. This would allow you to flexibly explore various constraints (e.g., constrain various correlations across the groups). You could also develop a model of the correlations and then constrain aspects of that model.
You could also check out the
metaSEM package in R which is designed for fitting structural equation models on multiple correlation matrices. The author of the package also has several articles (e.g., Cheung, 2008, Cheung and Chan, 2005), where he discusses the models and their implementation.
- Cheung, M.W.L. (2008). A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling. Psychological Methods, 13, 182-202. PDF
- Cheung, M.W.L., & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10, 40-64.PDF