My knowledge of this period is spotty at best, but isn't Crete and Cyprus a big thing at this point? Surely they'd make a useful ally and commercial partner?
Otherwise, I guess a standard alliance with Moab against Israel and Judea, with Moab getting the land east of the Jordan, and Edom the west. Take on Judea, and then if possible the Philistine States and suddenly Edom is in the position to dominate the region. If on good terms with Egypt, Egypt might even decline to intervene.
All the additional agricultural land would probably help the largely trade-based realm, and dominating the Philistine States should at least prepare the partnership for war against Isreal itself. Bit dicier that one, maybe an alliance with the Phonecians (who probably already trade with Edom).
After that, Edom has the agricultural lands of the Jordan Valley, its own trade, and a larger tax base to work with - and that should probably help. It probably still exists within the Egyptian sphere of influence.
But as I said, my knowledge is spotty. For all I know Israel/Judea were powerhouses in comparison.