Depending on what you are trying to do, I might got for a nVidia GTX (maybe a 1080 or better). This will give you 4 Displays (1 used for your system display)
And then add a DataPath (displayport) to the equation. The data path will take the 1 DisplayPort and give you 4 outputs (4k cut into 4 HD outputs).
This gives you the 4 outputs from the DataPath plus 2 direct from the nVidia card = 6
The Video Card direct connections could be further extended with Matrox tripleheads or more Datapaths.
** some AMD cards will give you 6 displays, so you still need to extend it (since you need a System/Operator display).
I believe nVidia cards on PC have been more thoroughly tested
My reason for this configuration is that it allows the Video card to keep all video onboard for output.
Sending it out via a BlackMagic card, requires moving the video from the Gpu to the output board, which is time consuming and will effect your performance.
Sending it directly out to an external device (datapath or Triplehead) doesn't require this extra step, and actually offsets some work to the external device.
If you are working with SDI, I recommend avoiding the Tripleheads. These have been a nightmare for me at times to get a standards compliant output.
(output would go Displayport -> HDMI -> HDMI to SDI converter. Often the HDMI signal would not be recognized by the SDI converter)