  We explore the behavior of collective nuclear excitations under a
multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements
have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp(-|H_{ij}|/V)$, with a
parametric correlation of the type $\log \langle H(x)H(y)\rangle\propto
-|x-y|$. The studies are done in both the regular and chaotic regimes of the
Hamiltonian. Model independent predictions for a wide variety of correlation
functions and distributions which depend on wavefunctions and energies are
found from parametric random matrix theory and are compared to the nuclear
excitations. We find that our universal predictions are observed in the nuclear
states. Being a multi-parameter theory, we consider general paths in parameter
space and find that universality can be effected by the topology of the
parameter space. Specifically, Berry's phase can modify short distance
correlations, breaking certain universal predictions.
