On the B744 that I fly we have:
TO, TO1 and TO2 available with TO1 being a 10% derate and TO2 a 20% derate.
Additionally assumed temperature can be used to give a flex thrust up to 25% less than the rating selected.
So, for example, we could achieve an 80% thrust takeoff using any of the ratings. But the V1 and Vmcg that we use would be different for each rating, because if we manually push the thrust levers fully forward we will get the thrust rating that we set.
We cannot use a flex thrust on a contaminated runway.
The company computer automatically calculates the "optimum" rating and assumed temp, unless we override it by demanding a particular TO rating.