Melody Notes as Chord Extensions
When harmonizing melodies, it can sound musically more interesting to place key notes of the melody higher up in the chord structure (like 7th, 9th etc.) than playing around root, third or fifth. Eg. you have a melody sequence of D-B-G: underlaying a straight Gmaj chord (D=5th, B=3rd, G=root) will sound pretty basic.
What would be more interesting would for example be Cmaj9 (D=9th, B=maj7, G=fifth) or even more fancy Fmaj7(#11/13) (D=13, B=#11, G=9). You set the melody in more interesting relation to the chord and even quite simple melodic sequences can sound very sophisticated like this. In this way, a huge palette of harmonization possibilities open up.
However, you should be aware that writing like this implies a certain musical colour palette and you should remain in there for a while. Jumping around between the above mentioned and some “basic” harmonization during the same melody will make your musical section lose musical integrity and sound random.