  We prove the existence of multiparameter isospectral deformations of metrics
on SO(n) $(n = 9$ and $n\geq 11)$, SU(n) $(n\geq 8)$, and $Sp(n)$ $(n\geq 4)$.
For these examples, we follow a metric construction developed by Schueth who
had given one-parameter families of isospectral metrics on orthogonal and
unitary groups. Our multiparameter families are obtained by a new proof of
nontriviality establishing a generic condition for nonisometry of metrics
arising from the construction. We also show the existence of non-congruent
pairs of isospectral potentials and nonisometric pairs of isospectral
conformally equivalent metrics on $Sp(n)$ for $n\geq 6$.
