I wanted to know if 7th, 9th, 11th and 13th chords can have both augmented and diminished forms. I'd appreciate your answers.
The note augmented or diminished in these chords is ^5. So C7+ will be spelt C E G♯ B♭. Cm7♭5 will be C E♭ G♭ B♭ - often referred to as C half-diminished.
The same works for 9ths, but it's confusing as the 9th part itself can be seen as diminished - as C7 with D♭ added, or augmented - as C7 with D♯ added (as in the 'Hendrix' chord).
Written names will help - C+7(♭9) or C9(♭5) make the actual chord very clear. And, of course, frequently, notes are omitted from 11th and 13th chords, which helps the sound blend, but not the naming...
So keeping any basic 7th, 9th, 11th or 13th chord with either an augmented or diminished 5th replacing P5 is permissable. In fact, any combination of notes will constitute a chord - just need to work out its function and note names to give it a title! But let's face it, some combinations don't sound good everywhere.
Yes, of course you can put any notes you like in a chord, so the question is more about naming convention.
Typically words augumented and diminished are used for triads only (at least in jazz/pop nomenclature). An exception is a fully diminished chord or diminished seventh chord 1 b3 b5 bb7, e.g. Eo7 (E G Bb Db).
Extended chords still can have diminished/lowered/flat or augmented/raised/sharp fifth, e.g.
- Em7b5 (E G Bb D) is minor-seventh chord with flat five, often called half-diminished
- E7#5 (E G# B# D) is dominant seventh chord with raised/sharp fifth
- E7b5 (E G# Bb D) is dominant seventh chord with flat fifth
- Emaj7#5 (E G# B# D#) is major seventh chord with sharp fifth