Edit a presentation while projecting

I am not an expert but it seems totally doable:

1. Try "detecting" your second display which is extending the screen. Go to System Preference > Displays > Arrangement Tab

2. Find the presentation software support menu check to see if the software allows you to have this type of functionality.

3. Have patience

First you need to make sure you are operating in Extended Desktop mode, not Mirroring mode. If you have the Displays icon in your menu bar, then you can turn off Mirroring from there. You can't use Mirror mode because it always shows the same content you both screens, so there would be no way to hide your actions from the audience. Extended Desktop means your Mac's screen is different from the external screen.

Once you are in Extended Desktop mode, use the feature in your presentation program that allows splitting the presentation across both monitors. I don't do those very much so I forget exactly what the options are called, but I know for a fact that both Keynote and PowerPoint have presentation options that do that, so your screen can show you both your slides and your notes while the audience only sees your slides.

What I am not sure about is whether you can actually edit as you present. While I know you can split the presentation so that you can see things your audience cannot see, this is only when the slides are being presented as a slide show. In order for you to edit, you must get out of slide show mode, back to normal windows and palettes. This will cause the slide show to stop on the big audience screen too, so they'll also see normal windows and other apps you may be running.

Or do you really mean you want to work in another application while you're presenting? That would be easier because you may be able to leave your presentation software in slide show mode on the big screen while you work on your screen. Again, this requires that you have Mirroring turned off.

You could also make two copies of the files with different names. Project one to the outer screen and edit the other on your screen. I think that would work.