Your NUC says it supports Mini-DP 1.2; HDMI 2.0; USB-C (DP1.2) http://ark.intel.com/products/89187/Intel-NUC-Kit-NUC6i7KYK
And DisplayPort - Wikipedia says DP 1.2 added support for MST, which should support up to 3 monitors.
But, this is all just what the documentation says. Perhaps one of the Intel support staff can confirm this.
Sorry I could not help.
This message was posted on behalf of Intel Corporation
To Al Hill: Thank you for the information.
tvy, in this case, the Intel® NUC Kit NUC6i7KYK supports 4K resolution in three displays connected at the same time (if using all the 3 video outputs, one per monitor/TV); however, if you want to use daisy chaining, the bandwidth will be divided into two monitors, therefore, 4K in two monitors at the same time using daisy chaining, is not supported.
You can use the following tool for supported configurations:
Hope this information helps.
Please don't hesitate in replying to this post if you need further assistance.