Luk 9:59 Follow me.
Go with me.
There three other times Jesus says these words, they are addressed to Matthew/Levi. In each of its four occurrences, the Greek is always the same.
The term "follow" means "to follow," or "go with," in a physical sense, but it is also a metaphor meaning "to be guided by" or "to follow the meaning of." The term also specifically means "to follow the thread" of a discourse.
The "me" is in the form of an indirect object, so it is not the object of "follow", which would be in a different form. The sense is that the person following does not act directly on the person they follow, but rather indirectly. The form has a number of uses in Greek. Most commonly it is an indirect object ("follow this road [the object] to Rome [the indirect object].
The eight primary uses (there are derivations) of the dative are:
1) the indirect object of an action-- "Follow to me."
2) the instrumental dative -- "Follow through me."
3) the location -- "Follow behind me."
4) to declare a purpose -- "Follow for me,"
5) a benefit "Follow for my benefit."
6) possession -- "Follow mine."
7) an agent -- "Follow by means of me."
8) a comparison -- "Follow like me."
In this case, since we are dealing with a person, not only are instrumental and agency more of less the same, but also purpose and agency are pretty much the same.