Local search as mutation operator

I saw that the applied mutation operators replace a primitive by a completely new randomly generated value. In my experience in genetic optimization tuning numeric parameters is sometimes faster when as an additional mutation operator a random factor (e.g. between 0.8 and 1.2) is multiplied to the existing parameter - so that a better solution is searched nearby a already good solution.

Is it planned or possible to extend manually the mutation operators to achieve that effect?