The next one is called
Modifications between ordinary natural transformations between functors between categories are trivial, but they exist between
between 2-functors between 2-categories.
The next one after that is called perturbation : a perturbation goes between modifications between pseudonatural transformations between 3-functors between 3-categories.
Beyond that, no established terms exists. Instead one starts numbering things and speaks of
n-Functors are 0-transfors.
Transformations are 1-transfors.
Modifications are 2-transfors.
Perturbations are 3-transfors.
And so on.