In this paper, we tackle the issue of making adaptive the reassignment of multicomponent signals using synchrosqueezing transforms. Indeed, depending on the frequency modulation of the modes making up these signals, the reassignment results with synchrosqueezing transforms are significantly different depending on the so-called order of the transform. In this paper, we introduce a new technique to choose locally the best order of the synchrosqueezing transform to represent a multicomponent signal, and study its behavior in terms of mode reconstruction on both simulated and real signals.