Hope all this makes sense :) I'll clarify via comments if necessary. Also, I am experimenting using bold text in this question, and will edit it out if I (or you) find it distracting. With that out of the way...

Using django.contrib.auth gives us User and Group, among other useful things that I can't do without (like basic messaging).

In my app I have several different types of users. A user can be of only one type. That would easily be handled by groups, with a little extra care. However, these different users are related to each other in hierarchies / relationships.

Let's take a look at these users: -

Principals - "top level" users

Administrators - each administrator reports to a Principal

Coordinators - each coordinator reports to an Administrator

Apart from these there are other user types that are not directly related, but may get related later on. For example, "Company" is another type of user, and can have various "Products", and products may be supervised by a "Coordinator". "Buyer" is another kind of user that may buy products.

Now all these users have various other attributes, some of which are common to all types of users and some of which are distinct only to one user type. For example, all types of users have to have an address. On the other hand, only the Principal user belongs to a "BranchOffice".

Another point, which was stated above, is that a User can only ever be of one type.

The app also needs to keep track of who created and/or modified Principals, Administrators, Coordinators, Companies, Products etc. (So that's two more links to the User model.)

In this scenario, is it a good idea to use Django's multi-table inheritance as follows: -

from django.contrib.auth.models import User
class Principal(User):
    #
    #
    #    
    branchoffice = models.ForeignKey(BranchOffice)
    landline = models.CharField(blank=True, max_length=20)    
    mobile = models.CharField(blank=True, max_length=20)
    created_by = models.ForeignKey(User, editable=False, blank=True, related_name="principalcreator")    
    modified_by = models.ForeignKey(User, editable=False, blank=True, related_name="principalmodifier")
    #
    #
    #

Or should I go about doing it like this: -

class Principal(models.Model):
    #
    #
    #
    user = models.OneToOneField(User, blank=True)
    branchoffice = models.ForeignKey(BranchOffice)
    landline = models.CharField(blank=True, max_length=20)    
    mobile = models.CharField(blank=True, max_length=20)
    created_by = models.ForeignKey(User, editable=False, blank=True, related_name="principalcreator")    
    modified_by = models.ForeignKey(User, editable=False, blank=True, related_name="principalmodifier")
    #
    #
    #

Please keep in mind that there are other user types that are related via foreign keys, for example: -

class Administrator(models.Model):
    #
    #
    #
    principal = models.ForeignKey(Principal, help_text="The supervising principal for this Administrator")
    user = models.OneToOneField(User, blank=True)
    province = models.ForeignKey(         Province)
    landline = models.CharField(blank=True, max_length=20)    
    mobile = models.CharField(blank=True, max_length=20)
    created_by = models.ForeignKey(User, editable=False, blank=True, related_name="administratorcreator")    
    modified_by = models.ForeignKey(User, editable=False, blank=True, related_name="administratormodifier")

I am aware that Django does use a one-to-one relationship for multi-table inheritance behind the scenes. I am just not qualified enough to decide which is a more sound approach.