From a currently running X11 session, I would like to provide/run a VNC server such that it appears to my system as a second, virtual monitor  i.e. so that I can position it using xrandr and drag/position windows onto it.How, if at all, could I achieve that?Edit: More info from OP in comments: Also asked here, without an answer. 
VNC-Server as a virtual X11 monitor to expand screen
vnc;xrandr;dual monitor
tl;dr: Force a virtual output of your gfx card to a display mode, and export that with x11vnc.You can achieve this, but there are a few prerequisites:A graphics card with multi-head capabilities (= can render several desktop surfaces). Which is most cards these days.x11vnc, a mature software (x11vnc) to export X11 surfaces (among others) to VNC clients.Most consumer cards these days can render several different outputs. Mine can do 3, out of the 5 that xrandr shows (eDP1,HDMI[12],DP[12]).Pick an unused output from xrandr, in my example HDMI2.Pick a resolution for the screen of the vnc client, and generate a mode: $ cvt 1920 1080# 1920x1080 59.96 Hz (CVT 2.07M9) hsync: 67.16 kHz; pclk: 173.00 MHzModeline 1920x1080_60.00  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsyncAdd that mode to xrandrxrandr --newmode 1920x1080_60  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsyncPut e.g. HDMI2 in that mode, and attach to the right of eDP1 (Main screen)xrandr --addmode HDMI2 1920x1080_60--output HDMI2 --mode 1920x1080_60 --right-of eDP1Now export that with x11vnc, choosing the appropriate offset:x11vnc -display :0 -clip 1920x1080+1600+0 <other options>Note: Add desired encryption/authentication/other options to that command.Now connect to with a VNC client to your virtual monitor. (or modify above command to connect to a listening VNC-client.