In certain cases you are (in your RTOW) limited by VMCG and/or VMCA because of short runway or contaminated runway.
The possibility to increase your max weight is to change the scenario you are dealing with everyday. That is to change your VMCG or VMCA value.
The only way to do it is to reduce power of the engine (flaps setting and altitude constant).
Normal VMCA and VMCG are calculated based on TOGA power and of course gives a certain yawing moment associated with. If you reduce engine thrust by a certain amount, then with every thrust setting you have new VMCG VMCA value (of course lower).
In that case you are still VMCG VMCA limited but your max toff weight is higher than the one with TOGA.
The other point is engine failure drill:
Why do not set TOGA if you really have an engine failure.
Because the speed you fly at (V2) is or may be lower than normal VMCA (calculated with TOGA power). Remember what happen if you fly near or below VMCA.