The idea of a closely related key is that there is a one-note semitonal shift that will yield a new scale, and this might imply a new root, and thus a new key.
I an extending this concept by first starting with any well-formed(see the article here) mode of the Major scale, and making a one-note semitonal shift that will yield a new well-formed scale of my own scheme of well-formedness. The results of such an exhaustive search are displayed below.
I should point out that since the Locrian scale(7th mode of Major scale) is not a well-formed scale under my own definition, it’s not included in my analysis.
In for each scale shown below, I labelled the parent scale, the mode by number and name, and the pattern in HWA notation. Out of all possibilities, there are ten parent scales, listed below. It’s interesting to note that all possibilities given below can be labelled by altering the 9th of the Major, Lydian, and Mixolydian modes, or by going to either a Major scale or a Mixolydian #11 at the Fourth or Fifth.