Number of distinct discrete eigenvalues of a self adjoint operator after compact perturbation increases.

Question

Let $T$ be a self adjoint operator on a complex separable Hilbert space $H$. Let $K$ be self adjoint compact operator. So, $T+K$ is also self adjoint operator. I want to know for what $K$ the number of distinct discrete eigenvalues of $T+K$ increases.

Is there any theory for the above question?

Thanks