BIAB currently supports a few 3 note chords which are not based on triads/thirds. such as C4 Csus and C5b.

With regards to C4 (spelt 1, 4 b7) it would be good to have the two other 4th based ones currently missing
(1 b5 7 and 1 4 7) Don't know what you'd call them but it would allow complete support for 4th based triads

You could extend this to triads built in seconds. 1 b2 b3, 1 b2 2, 1 2 b3, and 1 2 3.
This would help broaden BIAB's harmonic palette enormously with modern tone clusters standing in for Major Minor and 7th chords.

Alan