My understanding from the previous announcements/threads, DX12 will support multi-GPU from different vendors, in much the same way that Vista allowed AMD, Nvidia and Intel GPUs to be used together in a system. What I think is going to be the sticking point is getting AMD, Nvidia and Intel to play nicely together and write their drivers so they actually do work together. Also, DX12 and Mantle put the responsibility for the graphics performance a lot more in the hands of game developers rather than mostly in the hands of DX/graphics drivers, so we are then also relying on the game developer writing code that will work on multi-brand GPUs.
In short, from Microsoft's point of view, DX12 will allow multi-GPU from different vendors to work together, but I really don't expect to ever see it actually working outside of a few impressive tech demos. If a game actually supports it, I will be very, very surprised (and pleased).