Hm, let's see...
North Africa: African Crested Porcupine
West/Central Africa: Red River Hog
Southern Africa: another unique antelope, e.g. Gerenuk, Eland or Kirk's Dik-Dik; or - if Madagascar counts here - the Fossa. Secretary Bird?
North America: American Black Bear (I wouldn't actually be too happy to get them, but they're the only NA animal I can think of that would be a genuinely worthy addition at this point)
Central America: Collared Peccary
South America: literally any New World Monkey, but preferably either Howler or Spider Monkey
Arctic: Musk Ox or Wolverine
Central Asia: Takin
East Asia: Père David's Deer (another deer, and these are gorgeous animals!)
Southeast Asia: Lowland Anoa (we need a companion for the babirusa! plus they would be perfect for an islands pack)
Europe: Wild Boar or Red Deer (I don't actually think we need too many more species from Europe, but if we do get another one, it'd be between these too and the choice would depend on whether we get another deer/swine from another continent or not)
Oceania: Any Tree Kangaroo (although an Emu would be most essential here, and a wallaby, the kiwi and the tasmanian devil are very urgently needed additions in their own right)
They're not really listed here as categories, but also Blackbuck for South Asia/India and Gelada for East Africa.