A couple of extra thoughts on your multivariate data.
1. If the data is basically balanced, then the extenstion from
bivariate to multivariate will not change anything.
Balanced in this context primarily means complete data -
no missing values and equal numbers of offspring per sire.
2. Looking at the change from bivariate to say 5 variate analyses
will give you an empiracl feel for how much change is occuring.
3. It would be useful to do some principal components on the
full G matrix (you now have) to see how many negative roots
there are and maybe identify where the problems are in the matrix.