How many traits can a multivariate breeders equation handle?
Noting that the right hand side can also be written $\mathbf{G}\mathbf{P}^{-1}\mathbf{s}$, we see that the only theoretical limitation of the multivariate breeders equation is the invertibility of the matrix $\mathbf{P}$. This happens when the measures of two traits are the same for all individuals, making two columns of the matrix the same I.e. It becomes singular. 

This theoretical concern can become a practical concern quite quickly when multiple traits are measured. The solution is to effectively consider two traits as one.

The 'power' of the equation, by which I assume you mean something like 'accuracy of prediction', actually improves with the number of traits measured. Indeed, a big concern with measuring only a few traits is that the response to selection on those traits is actually 'caused' by selection on some other correlated but unmeasured trait.