I believe the Governing Body has suggested "together with them" in 1 Thessalonians 4:17 means that the living are raised during the same period of time as the dead in union with Christ, that is, during the Messiah's presence (parousia). The NWT seems to treat hAMA as a redundant term. Compare William Douglas Chamberlain's An Exegetical Grammar of the Greek New Testament, page 130. Chamberlain states that hAMA is redundant at 1 Thess. 4:17: he reckons that hAMA "shows the beginning of the retreat of SUN before hAMA."
BDAG indicates that hAMA may be used as a preposition with the dative to mean "together with . . ." It can also be employed pleonastically (i.e., redundantly) with SUN: "to denote what belongs together in time and place (about like Lat. UNA CUM) . . ."
The Latin UNA CUM also means "together with."