All seven modes can be applied to seventh chords in order to embellish and add texture to your melody lines.  This concept is related to chord scales.  Each of the perfect chord scales is related to a particular mode.

Watch the video below to learn how to derive chord scales for Seventh Chords:

Major Seventh Chord
If we use Cmaj7, the chord tones are C-E-G-B, and the tensions are D-F#-A (2-#4-6 or or 9-#11-13).  Those notes, C-D-E-F#-G-A-B (1-2-3-#4-5-6-7), make up C Lydian.  Those notes are found by building a major triad one major second above the root (D-F#-A).  If we build a minor triad (D-F-A) one major second above the root (2-4-6 or 9-11-13), we get C Ionian.

You can play either Lydian or Ionian over your major seventh chords. 

 

Minor Seventh Chord
If we use Cmin7, the chord tones are C-E-G-B, and the tensions are D-F-A.  Those notes, C-D-E-F-G-A-B, make up C Dorian.  Those notes (D-F-A) are found by building a minor triad one major second above the root (2-4-6 or 9-11-13).  You can also build a major triad (D-F-A♭) one minor second above the root (♭2-4-♭6 or or ♭9-11-♭13), giving you the notes C-E♭-G-B♭-D♭-F-A♭ (1-♭3-5-♭7-♭2-4-♭6), or C Phrygian.  Or, you can add a diminished triad (D-F-A♭) one major second above the root (2-4-♭6 or 9-11-♭13), giving you the notes C-E♭-G-B♭-D-F-A♭ (1-♭3-5-♭7-2-4-♭6), or C Aeolian.

You can play either Dorian, Aeolian, or Phrygian scales over your minor seventh chords. 

 

Dominant Seventh Chord
If we use C7, the chord tones are C-E-G-B, and the tensions are D-F#-A (2- #4-6 or 9- #11-13).  Those notes are not equivalent to any standard mode.  Instead of building a major triad, build a minor triad (D-F-A) one major second from the root (2-4-6 or 9-11-13), giving you the series C-E-G-B-D-F-A, or C Mixolydian.

You can play a Mixolydian or Mixolydian#11 (Lydian Dominant-fourth mode of the Melodic Minor scale) scale over your dominant seventh chords.

 

Half-Diminished Seventh Chord
If we use Cmin7(5), the chord tones are C-E-G-B, and the tensions are D-F-A♭ (2-4-♭6 or 9-11-♭13).  Those notes are not equivalent to any standard mode.  Instead of building a diminished triad, build a major triad (D-F-A), a minor second from the root (♭2-4-♭6 or ♭9-11-♭13), giving you C-E-G-B-D-F-A, or C Locrian.

You can play Locrian or Locrian Natural 2 (sixth mode of the Melodic Minor Scale) over your half-diminished seventh chords.