How can I edit a presentation while in presentation mode?

For Windows:

PowerPoint has had this capability for quite some time. The key is to NOT duplicate your computer screen with the presenting screen (TV, projector, other screen, etc. I'll use "projector" in this how-to for simplicity purposes.) The only requirement is that you have some screen besides the projector.

With a Windows computer, when you connect to a projector use the Win + P command and choose the Extend the display. This means that your computer screen and the projector will show different things. You can also do this in Display Settings if you're more familiar with that.

PowerPoint has some intelligence to determine which screen is a projector and which is not, but if you need more control over which screen the presentation is on and which one will be your control screen, in the Slide Show tab you'll find Set Up Slide Show, which includes settings for this.

Another thing to keep in mind is that Presenter View (also an option in the Slide Show tab) can make things a little more difficult, but not much. When using Presenter Mode, the default behavior is for the Presenter Mode window to go full-screen, and you cannot edit in Presenter Mode. However, resizing the Presenter Mode window should allow you to easily bring up the main PowerPoint window, which is where the magic will happen.

So, all that aside, the meat of the solution:

Just edit the darn thing. That's all it takes.

With the presentation running happily away on the projector and the main PowerPoint window up on your computer screen, you can edit as much as you please and your edits will be reflected in real-time in the presentation itself (Note: I've known about the Presenter Mode and running presentations on multiple monitors for years, but am only testing the specifics of editing in PowerPoint 2016. I do not know how the behavior is different in previous versions.).

For Apple:

I don't know. I could not find specific documentation of this ability/feature for either Keynote or PowerPoint for Mac. While in Windows the Presenter view can be resized, some suggest this is not an option in Office for Mac.

One work around would be to use the Freeze capability of most projectors to freeze the current image on the screen, then exit the presentation on the computer, edit the slideshow, begin it at that slide again, and then unfreeze the projector image.

For Mac using PowerPoint 16:

Open the presentation you want to show. On the Mac menu bar go to window and click New Window.

This will pop out a duplicate PowerPoint presentation. Drag one of them to the second monitor and run it under setup option: "Browsed by an individual (window)"

You can now edit and add slides on the fly in the window that remains on your main desktop without interrupting the presentation. You can even edit the slide that you are currently showing on the screen and it will update automatically as you change it.