Improvisation on dominant chords is maybe the first to be learn by improvising musicians. Dominant chords are frequently embellished by all kinds of extensions so any musician must be familiar to the modes he/she would play on them.
• The blues scale may be played on chords that include the 9th and the 11th and on the 7#9 chord.
• The most popular mode on 7,9,(11, 13) is the mixolydian mode . For instance, on a C9 chord you may play C mixolydian (the 5th mode of the F major scale).
• The half - whole tone scale may be played on 7b9 and 7#9 chords with a major 6th. On C7b9 and C7#9, try C 1/2, 1.
• Whole tones scales may be played on 7#11 chords like C whole tone on a C7#11 chord.
• Phrygian major can be played on 7b9 chords with a minor sixth. On a C7b9b13 chord, you can try C phrygian major (the 5th mode of F harmonic-minor).
• Mixolydian b6 also works on 9b13 chords. Try on C9b13 C mixolydian b6 (the 5th mode of F melodic-minor).
• Superlocrian works on 7#9 and 7#9b13 (altered chords). On C7#9(b13), you can try C superlocrian (the 7th mode of C# melodic-minor).
• Lydian b7 may be played on 7,9#11 (or b5) chords. On C7,9#11, you can play C lydian b7 (the 4th mode of G melodic-minor).
In conclusion, we've got the blues scale, a diatonic mode, the two symmetrical scales, a harmonic-minor mode and three melodic-minor modes. Musicians play so much on dominant chords so they get used fast to all their extensions.