Leo77,
Your original post has lead to some interesting twists. If you are doing a REDUCED thrust takeoff (i.e. Flex takeoff), you can have full confidence in advancing the thrust to the engine rating, because VMC has been calculated for this. I think John Tullamarine's warning related to a too rapid advance of thrust which may not be caught by the pilot, I've seen this.
The point I was making (2 posts ago) was that some engines have multiple ratings, with associated multiple VMCs. Reduced (Flex) thrust may be allowed for each of these Ratings, and, if an engine fails, the thrust may be confidently advanced to the rating, NOT to maximum (unless that was the rating used). A similar situation exists for those aircraft with permitted overboost (APR). (We're not talking about a engine limit exceedance here, as might be the situation in a wind shear recovery).
An example of this - The B777 / Trent uses 20% derate (80% of maximum) thrust for operation on icy / slick runways. This significantly reduces VMC (highly desirable on icy / slick runways), allowing much lower V1s than for Full rating. If, following engine failure on an icy / slick runway just above V1, with a long acceleration to Vr to follow, thrust were advanced above the 80% Rating, to the full 100%, a directional control disaster is in the making. Advancing to the 80% Rating from a lower 'flexed' setting should cause no problem, as long as the pilot anticipates the extra swing.
There's a big difference between Derated thrust, and Reduced thrust (Flex).
Smokey