Generator sets should not be overloaded once running, but are designed to take an overload condition for a very short time during start up of the set. If a set is running for long periods of time with an overload condition (that is a rating above the maximum rating of the set) various things may occur.
These include such things as:
Overheating of the coolant system
Overheating of the alternator windings
Oil viscosity (thickness) break down resulting in low oil pressure
A shortening of the working life of the generator