[FEN "qn1r2b1/1N1BpRn1/1p3bP1/rN1K2Br/P3P2p/nR1N1b1P/b2r1P2/k7 w - - 0 1"]
Here is an (ugly) suggestion wth 29 units.
White is stalemated with 8 pins; removing any Black unit would break the stalemate.
White has promoted one of her three missing pawns (to knight) and black has promoted all of her five missing pawns (two into rooks, two into light-squared bishops, and one into a knight).
The three captures (wQ and one pawn of each colour) ensure that this position is reachable. I am pretty sure we could add at least one of the missing pawns but that would require some retrograde analysis to prove the legality of the position that is beyond both my motivation and my available time. For instance, adding a wP on b2 doesn't work because it won't be possible anymore to promote all bPs.