So the other day I was looking through the Ted Greene chord books seeing some really great progressions and chords that I was really having trouble finding the origin of. I wanted to try to find some theoretical basis for some of the chords that weren't built from the major scale and its modes. I started thinking that chords with alterations were basically just chords that were being borrowed from other scales, meaning there was a temporary shift in "key."

My thinking was that if you were playing in a major key, you could substitute chords from the other scale at times in order to get the sound of that scale, while still maintaining the coherence that the major scale offers. My thinking was that if you were taking chords from a scale that wasn't too different from the major scale, the substitutions mixed with the right voice leadings wouldn't be as jarring as those taken from a very tonally dissimilar scale.

So, first things first, here are the major modes:

Ionian: (1-2-3-4-5-6-7)
Dorian: (1-2-b3-4-5-6-b7)
Phrygian: (1-b2-b3-4-5-b6-b7)
Lydian: (1-2-3-#4-5-6-7)
Mixolydian: (1-2-3-4-5-6-b7)
Aeolian: (1-2-b3-4-5-b6-b7)
Locrian: (1-b2-b3-4-b5-b6-b7)

For chords that aren't far removed from the major scale, here are the harmonic minor modes, since only one note has been altered to get them from the major modes:

Ionian #5: (1-2-3-4-#5-6-7)
Dorian #4: (1-2-b3-#4-5-6-b7)
Phrygian Dominant: (1-b2-3-4-5-b6-b7)
Lydian #2: (1-#2-3-#4-5-6-7)
Altered bb7: (1-b2-#2-3-b5-#5-bb7)
Harmonic Minor: (1-2-b3-4-5-b6-7)
Locrian nat. 6: (1-b2-b3-4-b5-6-b7)

The reason I have Ionian #5 as the first mode is because it wouldn't make sense to have a minor mode set as the first degree if you're playing in a major key. If you were playing in a minor key, it would be a different story.

If you were playing in C major, you could theoretically substitute a chord built from one of the corresponding scale degrees of C Ionian #5. The exception to the rule is of course chords built from the Altered dominant bb7 scale, which would be built on G# instead of G.

Chords taken from the modes of Lydian Augmented (melodic minor), would probably be slightly harder to the ear, since the melodic minor scale is the result of altering two notes of the Aeolian/natural minor mode. Of course there's also the fact that there is an F# and a G# in the C Lydian augmented scale.

Lydian Augmented: (1-2-3-#4-#5-6-7)
Lydian Dominant: (1-2-3-#4-5-6-b7)
Mixolydian b6: (1-2-3-4-5-b6-b7)
Aeolian b5: (1-2-b3-4-5-b6-b7)
Altered Dominant: (1-b2-#2-3-b5-#5-b7)
Melodic Minor: (1-2-b3-4-5-6-7)
Dorian b2: (1-b2-b3-4-5-6-b7)

To take it to the extreme, you could theoretically take chords from several different scales, but that would most likely be hard on a listener's ears. You could also take chords from a scale that is very different from the major scale, such as the Enigmatic scale, or even a scale that contains more or less than 7 notes.

I don't know. I just thought I'd get a few opinions and maybe some extra information on the subject.
Yeah - you're right, you can substitute one chord for another when both chords share the same function. The most common chord to substitute is a V chord, and a lot of the time the V chord in a major progression (at least in jazz) is substituted with a chord of the same function from a different scale.

Instead of G7 from Ionian, you might use G7b9 from Phrygian dominant, G7#5#11 from the whole tone scale, G7alt from the altered mode, G7#11 from Lydian dominant and so on and so forth. (There are certain guideliness people follow here to know when to use what chord, for example - the only time I substitute V from the major scale with V7alt from melodic minor is when the third of the chord is not in the melody). You're taking a chord that doesn't appear in major scale harmony and substituting it with one that does, the only thing that the remains is the function of the chord is still the same.

With dominant chords, the alteration that is added is normally done so on the premise of how the chord resolves, because while adding alterations doesn't affect the function of the chord - certain alterations do resolve in particular ways. If the chord was resolving down a fifth, you might choose V7b9 over V7#5#11. If the chord resolves down a fourth, V7#11 is the best choice.

Often people will reharmonize a major ii - V - I progression that starts out like a minor ii - V - I and ends up like a major progression just by borrowing chords. Instead of D-7 - G7 - CΔ, it's common to see Dø - G7alt - CΔ, or Dø - G7b9 - CΔ.

Something else which is common (doesn't really include extensions/alterations though) is substituting chords that function as a tonic chord. If you see a chord progression that includes a minor 7th chord that isn't part of a ii - V or bII - V progression, then the minor seventh chord is functioning as a tonic minor chord and can be substituted for D-6, D-Δ and so forth. Another rule here is that if the minor seventh note is present in the melody, the chord should remain a minor seventh chord.

The tonic major chord is often substituted with the lydian chord (CΔ7#11 instead of CΔ, it's often substituted with the Δ#5 chord from Lydian augmented that you mentioned (CΔ#5 instead of CΔ although there are certain 'rules' for this kind of substitution that include points I made earlier about what notes appear in the melody... but in short, yes you are correct and it will work - but each situation is different, and the chords you change will almost always be determined by the melody (or the other way round, you may change the melody to fit the new chords).