is it possible to define an extension method that at the same time is an operator?
I want for a fixed class add the possibility to use a known operator that actually can\'t
No, it is not possible to do from outside of the class. ++ operator should be defined inside class which is being incremented. You can either create your own class which will be convertible from string and will have ++ overload or you can forget about this idea and use regular methods.