I would say yes. While in normal circumstances electrons are being first removed from the outermost shells, it is also possible to ionize an atom by removing electrons from inner shells (google Auger effect), and I see no reason why you couldn't remove more than one.
That being said - such excited ions have very short lifetime and probability that the other electron would get kicked off in this particular time period if extremely low. So while there is no reason why such an excited ion could not exist for a tiny fraction of a second, there are practical reasons why such an ion would be never produced.
I can be wrong though.