Is it possible to alphabetize a sorted view? Drupal 7.18 w/ Views 7.x-3.8 user here. 

I have a view set up that consists of rows of objects, which have names and 'yes/no' properties. By default, it is sorted alphabetically by object name. I want to allow the user to be able to sort through the view using the various properties, but to then have those sorted results be alphabetized for them post-hoc. Currently, when the user sorts through the view using property X (with either 'yes' or 'no' content), the objects seem to be retrieved based on their location in the database table, or some other factor. Either way, they are in no way alphabetical which means that this view of 500+ results is impractical to sort in this fashion. 

So, is it possible to set up a sort mechanism where the results are (1) sorted by property into their respective 'yes'/'no' groups (or any other groups with identical content for that matter) and then (2) alphabetized?

To demonstrate what I mean, I currently have something like this:

NAME    PROPERTYX
Alpha   yes
Beta    no
Delta   yes
Epsilon no
Gamma   yes


Which when sorted using PROPERTYX (let's say descending), might return something like:

NAME    PROPERTYX
Delta   yes
Alpha   yes
Gamma   yes
Epsilon no
Beta    no


(As I said, I suppose this random order is based on the object's actual location in the database table.)

When the desired output would be:

NAME    PROPERTYX
Alpha   yes
Delta   yes
Gamma   yes
Beta    no
Epsilon no


Can this be accomplished somehow?
It is definitely be possible to add a second sort to the query which will give the desired effect, but you will have to write some custom code.

There are several hooks that Views provides that you can use in a custom module.  I suggest looking at hook_views_query_alter().  The example code on the API page actually shows it altering a WHERE clause, but creative use of dsm()'s will help you figure out what you need to change.

I'm sorry that I can't give you code (because this kind of modification is highly specific to your installation), but this is definitely the way to go.