I have an NVIDIA GTX 1070ti Gaming 8G and I can confirm the DSR solution posted above absolutely works. I tried to use an external 4k->1080p scaler and it worked, but my card was not powerful enough to display two 4k signals at the same time with ultra resolution on my golf simulator game, TGC 2019. Without the scaler, my card kept downgrading the 4k to 1080p to match the monitor. Once I used the NVIDIA solution with DSR, I'm set, card can handle the 4k/1080p cloned signal and still perform! Very cool, thank you for posting!
I have two projectors and a touch screen monitor running off one card. The 4k projector and a 24" 1080p touch screen are duplicated/cloned, while the other 1080p projector is extended. The 4k projector gets a 4k signal and the others get a 1080p signal.
Note, it does take a little fiddling around in order to get it working properly. First you need to set up DSR per the instructions above, then right click on the display in the NVIDIA control panel (resolution setting) and clone one of the displays. Make sure the 4k display device is the clone source. Then select the DSR resolution that says 4k/1080p/4.x. Eventually both the 4k projector and the 1080p monitor will show 4k/1080p/4.x resolution. Note, I use the windows key+P to set the duplicated 4kprojector/monitor as primary, or the separate 1080p projector as primary.
From what I can tell, DSR is like a proxy for resolution. It tells the computer and the games/applications that your display can accepts 4k signals, so I can set 4k in the game. Then on the HDMI/display port outputs it uses EDID to gather the metadata detailing the capabilities of the display (4k, 1080p, etc), and down-converts the 4k signal to 1080p when necessary. I also believe the 4k signal is being maintained for a device capable of displaying that resolution. Reason being is when I check this signal on my 4k projector it shows 3840 x 2160, and when checking the same on the 1080p it shows 1920x1080. Secondly, there is a slider to adjust DSR sharpness in the NVIDIA control panel. When I move that from 0%-100% the sharpness changes on the 1080p monitor, but not on the 4k projector, which tells me DSR is working on the monitor, but passing the 4k signal straight to the projector. No extra hardware required. Here is an explanation of the down-scaling from NVIDIA: https://www.geforce.com/hardware/technology/dsr/technology
This works 100%, what an awesome feature from NVIDIA!