I use a keyboard shortcut to push or pop the window under the mouse on Linux all the time.
It appears that MacOS does not have that feature, so I wanted to see if KM might do the trick. Can anyone confirm if that's possible with this program?
Thanks
I'm not really sure what you mean by "push or pop". If "push" means "send this window to the back", then:
Send Window Under Mouse to the Back.kmmacros (21 KB)
If "pop" means "bring this window to the front", then doesn't simply clicking the window do that? It's likely I've misunderstood.
You've got it. I just know I liked using the hot keys to reorder the windows to find the one I'm after without having to take my hands off the keyboard. Thank you for the information. Looks like I'm going to have to buy the program. 
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Ah ok. The macro above was based on this comment and requires the mouse to be placed.
If you don't want your hands to leave the keyboard, just remove the mouse click action and the macro will send the current front window to the back. It's a bit laggy as KM doesn't have a "send to back" function for window management, and we have to use AppleScript.
If all you want to do is cycle windows, is there any reason why you don't want to use the standard hotkey ⌘` for that?
This macro appears (from the screen shot) to only work with windows of the frontmost app. It does not do what the OP wanted, if the OP was thinking about a mix of applications (which is not clear from the question, but might be presumed).
Has anyone come up with any tricks for pushing the frontmost window behind windows of other apps?
Hi, @August. You might want to check this thread: Send the front most window to back? bring the back to front?
Thanks. Both that thread and this one:
only work with windows of the same app.