SLI (nVidia) and Crossfire (AMD) are intended for 2 of the same cards.
AMD allows it's lower cards to be run with "Dual graphics" and paired with the integrated GPU in their APU's, but it didn't offer much of a performance boost. or Crossfire with cards that have the same GPU architecture.
nVidia is much stricter with SLI and it must be the same GPU and the motherboard has to run them no less than PCIe x8 slot.
While you can't run both, the 480 will be a very nice upgrade over the 960. The 960 was slower than the R9 380 and the 480 is around the 390 and 970 performance. You could sell the 960 and see if that gets you to maybe a GTX 1070, which would be a huge jump.