another alternative is to get away from standard guitar tuning.
this enables more options,with ease,for modal dyads,or chords without major or minor third,although these can be added if wanted when in a modal tuning.
next,look at different inversions,for example bars 4 and 5 Staten Island,instead of using e minor,one could use e modal,or a two fingered a7 shape, 002020 slid up to fifth fret 005050 ,giving you the notes
eaggee,this could be used instead of the conventional a7 shape.
the problem is that many accompanists do not experiment or are often unaware of all the different inversions available