Compound German verbs are formed as
prefix + basic verb
So, if you have the verb X you can have its compounds by adding one prefix to it.
I'm asking whether a certain prefix carries always the same added meaning, whatever the basic verb you add it to. In English, this is usually the case (e.g., go, undergo, forego...).
If this is not the case, can you provide examples of prefixes whose added meaning changes according to the verb it is used on?