Can you have too much exhaust ventilation?

It is possible to have too much exhaust ventilation.

Yes. If attic exhaust exceeds intake it's possible that the exhaust vents will pull its needed intake air from itself (if they are ridge vents) or from a nearby vent (if they are wind turbines, box vents) or from the living space (if they are power fans). This can lead to inefficient attic airflow across the board and possibly weather infiltration (depending on the exhaust vent involved and the circumstances). Bottom line, it's best to balance the attic ventilation 50% intake and 50% exhaust.