Please feel free to emend this if I have not described my question cogently. Though knowing little of Latin, I have exemplified with it because I have encountered it more than Ancient Greek.
For example, in Latin, in addition to their (usual) meanings as prepositions, many common prefixes ad-, com-, de-, ex-, re-, etc... serve as intensive prefixes, but for a given verb, what motivated or induced the prefix used? Was a prefix chosen randomly?
Or does each intensive prefix uniquely connote or imply an especial, particular intensification?