Is there any molecule describable by three-level with mixed parity and transition dipole moments in different directions?

I would like to know if there are molecules described by a three-level system with mixed parity and transition dipole moments in different directions. By mixed parity I mean all three transitions can be excited by electric field. In principle I don't think such a system is forbidden, but it would be perfect if there are some examples. Does anyone have an idea? Thanks!


