Keynote Play presentation on 1 display and Just see my desktop on my second

Is there a way to have keynote play full screen on one display and just let me have access to my desktop on a second display? It always shows the presenter notes. I want to just be able to access my desktop while the presentation is running.

I had a similar problem and found a surprisingly simple workaround on the Apple Support Forum (https://discussions.apple.com/thread/5522746?tstart=0)

I needed a way to show my presentation on a webinar and still have access to the webinar control panel so I can see questions when they come in without having to close the presentation first.

The SOLUTION: You basically just need to export your completed Keynote presentation as an HTML file and open it in a browser. Then simply make it full screen on the screen or projector you're showing it on.

I used Chrome and found that the address bar still appeared in full screen view. To fix this I simple unchecked the "Always show toolbar in full screen" option in Chrome's View menu.

Solved the problem for me. Transitions worked too.

I know this thread is pretty old but I hope that helps someone searching for help with now (like I was)

This issue has been bugging me for ages. However, Apple has finally updated Keynote, half-assed but still.

In Keynote 10.1, there is finally the Play > Play Slideshow in Window option which does exactly that.

You'll have a window (where still the window bar shows up when you move the mouse, well done Apple!) with your presentation, you can resize it and move it wherever you want, share it with Zoom or another video conference tool and still be able to see your Desktop.