Alternative Chord Structures
The structure of having a chord consisting of root, third, fifth etc. is nothing that is written in stone. Alternative chord structures may have a very interesting and useful sound and still sound like a fully working chord.
A nice field for experimentation is building chords from intervallic ideas. Breaking up the standard of structurizing a chord in thirds might help to find interesting chords. Probably the most commonly used alternative structure is to create chords from fourths, fifths etc. But also symmetrical patterns like M2-M3-M2-M3 (e.g. C-D-F#-G#-C) might result in interesting sounding chords.
The interesting thing with such chords is that they most likely will be harmonically ambiguous. The chord above could for instance be seen as a G#7(#11), a D7(#11), a thirdless Cadd9(#5#11) or a thirdless F#add9(#5#11). In any case, standing on its own it suggests a whole tone scale. However depending on how you decide to fill up the gaps with a scale (e.g. deciding whether to play an A or an A# in a melody on top), you can change its scale impression. This ambiguousity will result in interesting musical possibilities if you consciously use it to your advantage. There are practically endless possibilities finding interesting harmonic sounds with these strategies.