In practice this is numerically unstable and it's generally better to use methods that use a larger and orthogonal subspace (i.e. Krylov methods) to get multiple eigenvalue/vectors. In nuclear reactor problems you can maybe get about 5 eigenvalues by filtering the larger ones but after that it gets noisy fast. I've gotten up to 1000 good eigenvalues from a large neutron diffusion problem using Arnoldi.