No chord within a chordal structure is an extension of another........sure it is when you start dealing with higher sinorities. Take Cmaj9, within this chord you have a C triad, an E minor triad, and a G triad. As Griphon noted before (I think) a 4,5,1 prog can be thought of as a ii-7 (minus the root)5, 1. Piano players think like this all the time, a G triad in the left hand with a F triad in the right hand would produce a G11 chord.