Perhaps 'The essence of multivariate thinking' by Lisa Harlow. (Multivariate regression is MANOVA, or rather MANOVA is multivariate regression, so a book that covers manova should do it.)
I generally try to avoid multivariate analyses of this sort, and I cite:
Huberty, C., & Morris, J. (1989). Multivariate analysis versus multiple univariate analysis. Psychological Bulletin, 105: 302-308.
When I do it.
More recently, there's a tendency to think of multivariate analyses as special cases of either structural equation models or multilevel models. If you understand one of those two, it's more straightforward to think about the analysis in these terms.
Jeremy