Good morning.
De-rate limitations are related to how de-rate is achieved. If it's a FADEC selection option and the maximum available thrust following an engine failure is limited downstream of the thrust levers, you tend to get fewer restrictions. If, on the other hand, it's an N1 setting and you can push the thrust levers beyond the de-rate position to get full rated thrust, then expect limitations.
Why? Because, unlike assumed temperature thrust reduction (flex), de-rate certification is the whole program, including Vmc for the lower thrust setting. Because V1 and, by association, other key speeds are tied to Vmc, it is possible to have a V1 and V2 at the de-rate thrust that would lie below Vmc at fully rated thrust. Lose an engine, select fully rated thrust and you may have a problem.
Certain national authorities may place further restrictions on the operational use of de-rate. For example, on low friction runways, weight drops as V1 does, until you get to Vmcg and V1 can't drop any further. At this point, you can see a precipitous drop in weight as runway length declines. Using a de-rated thrust, with lower Vmcg, permits a lower selectable V1, so weight decrements will fall more gradually until you hit the lower Vmcg. In this window, from the full-rating Vmcg to the de-rate Vmcg, it will be possible to lift more weight at de-rate than at full thrust.
Some regulators don't like the math of this method, depending on the degree of suspicion they place on the manufacturer's methods for performance calculations for wet and contaminated runways. In these cases, you may see a further restriction prohibiting takeoff weights in excess of what can be lifted at full thrust. Clearly, manufacturers and operators dealing with these regulators are not happy about it.....
Vs