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11th Chord and 13th Chord
To get extended 9th, 11th, and 13th chords, all you do is stack more thirds atop the underlying 7th chord.
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If you stack a third on top of a 9th, you get an 11th chord:
C11 = C E G B♭ D F
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If you stack a third on top of an 11th, you get a 13th chord:
C13 = C E G B♭ D F A
Now you’ve got six- and seven-note chords. So you need two hands to play them on the keyboard. As for six-string guitar, to play a 13th chord, you have to leave out one of the notes (normally the 11th).
Your brain processes 9th, 11th, and 13th chords as though they’re some fancy species of 7th chords. All such chords are dissonant.
Just keep in mind that all chords are triads and sevenths, or variations of triads and sevenths.
These extended chords are common in jazz and romantic music of the 19th Century.