Certainly. Put the atom in an external electric field, for example, and the Stark effect will tend to split degeneracies. Similarly, the Zeeman effect does the same for a magnetic field.
So stark effect and zeeman effect affect the degeneracies of orbitals... But what about the atom then? How can it be stable? Moreover, stark effect and zeeman effect contributed for the evolution of degenerate orbital concept (I suppose)...