DX11 Crossfire will not work with those cards.
However two different cards should be able two run together in some titles in DX12 MultiGPU.
Ashes of the Singularity / Escalation (also known as Ashes of the Benchmark) is one example.
DX12 MultiGPU should run on the DX12 mode of Ashes of the Singularity and Ashes of the Singularity Escalation.
It used to work well with a pair of R9 Nanos and showed reasonable positive scaling (higher framerates) .
It also ran with R9 Nano + Nvidia GTX790Ti in the past.
It showed better performance with the AMD card in the primary PCIe slot.
Although it did work in the past, my R9 Nanos have shown negative scaling for all resolutions and modes I have tested for over a year now with various AMD Drivers. I have reported this to AMD here on the forum and using Reporting Form.
I have seen examples of people running different AMD cards in DX12 MultiGPU on Youtube.
I think it was DX12 MultiGPU in Hitman,
There are still very few DX12 titles available though.
DX12 MultiGPU runs well for me on a pair of R9 Nanos or R9FuryX/Nano on the DX12 titles I have run that support it.
If you need better performance in gaming and you do not have another good reason to have more than one GPU (such as Blender rendering, OpenCL Compute, Mining) you would be much better to get a single high performance GPU.