Unmodalize Dialogs (Make Modal Dialogs Non-Modal)

Harrymc pointed out, that AutoHotKey might be able to unmodalize windows, which lead me to this question that contained the following AHK script (with a minor syntax error which was fixed in below version):

^e::
MouseGetPos,,, WindowUnderMouse
WinSet, Style, -0x8000000, ahk_id %WindowUnderMouse%
return

With AutoHotKey installed, save this script in a file.ahk, double click the file (or right-click and select Run Script). If you have a modal dialog and want to interact with its parent/background windows, hover the mouse over the parent/background window and press CtrlE (that's what ^e::) stands for; the background/parent window should now react to interaction again without closing the modal dialog.

The "styles" are documented here. -0x8000000 is documented as

WS_DISABLED | 0x8000000 | +/-Disabled. Creates a window that is initially disabled.