| Sus4 chords occur in diatonic harmony, same with minor 7 (11) and also aug chords (well, maj7(#5) chords which are built on the augmented triad.
For sus4 chords, I'll direct you to the thread that KayCee posted. They're typically used as a substitute for the V7 (or V) chord, or the ii-7 chord in a tonal situation. They have a lot of other uses too.
Minor 7 (11) chords are functionally exactly the same as regular minor 7 chords. This is really an important concept to keep in mind, because it simplifies a lot of things in thinking about harmony. That 11 is just a color tone, or tension, and serves no functional purpose besides just to make it sound denser, richer or "jazzier". In a diatonic situation, all the color tones must be diatonic as well, and it just so happens that with minor 7 (11) chords, every diatonic minor 7 chord (II-7, III-7, VI-7) has an 11 that fits the key. If it were a minor 7 (9), chord, however, you couldn't use it as the III-7, because the 9th degree of a III-7 chord is not in the parent scale (it would be a #4 in that key).
A good way of looking at what color tones tones you might have in a diatonic situation is by looking at the tones of the basic triad and then seeing if the note in the scale above it is a whole tone, or major 9th above it. If it is, its an available tension, if it isn't, it can't be used in the chord. For example, in C major, you have a Imaj7 chord with the triad C E G. D is a major 9 above C, so you can use a 9 on a Imaj7 chord. However, F is a minor 9th, or half step up from E, so you CAN'T have a Imaj7 (11) chord (try playing one on the piano, it sounds really, really harsh). A is a major 9th above G, so you can have a 13 on a Imaj7. That means that in a diatonic situation, you can have Imaj7(9), Imaj7(13) or Imaj7(9,13).
Aug chords typically don't exist in a diatonic situation (although they can, as the III chord in harmonic minor or melodic minor keys). Usually, they function as dominant V chords, coupled with a minor 7th on occasion. A very typical V to I cadence can be spiced up a little bit by making it a V+ to I cadence. The augmented 5th of the augmented chord voice leads really nicely to the major third of the I chord, giving it a little extra chromatic oompf. It has a little more tension, and a little more color than the typical V chord.
You'll find that non-diatonic harmony is a huge field of study. You might need to specify exactly what you're looking for.
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