Enhanced mesoscopic fluctuations in the crossover between random-matrix ensembles

In random-matrix ensembles that interpolate between the three basic ensembles ~orthogonal, unitary, and symplectic!, there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such correlations, using a remarkable correspondence between the interpolating ensembles late in the crossover and a basic ensemble of finite size. In small metal grains or semiconductor quantum dots, the correlations between different eigenvectors lead to enhanced fluctuations of the electron-electron interaction matrix elements which become parametrically larger than the nonuniversal fluctuations.