Take an A320 for instance. Minimum crew is 4. If a crew member is sick or injured downroute then there is a special dispensation to reduce crew compliment by one but only if pax figure is reduced to max 150. This dispensation can only be permitted away from a crew base.
For an A319, and presumably a 320 too, three crew operation (1 crew member per 50 pax) is permitted but max capacity of 150.
This is the case in the UK anyway.