Combine the flour, baking powder, salt, and baking soda in a bowl.
Using a stand mixer fitted with a paddle, beat the butter, shortening, and sugar on medium-high speed until pale and fluffy, about 3 minutes.
Add the eggs, one at a time, and beat until combined.
Reduce the speed to low and add the flour mixture in 3 additions, alternating with 2 additions of the reserved coconut-buttermilk mixture, scraping down bowl as needed.
Add ¾ cup of pecans and give the batter a final stir by hand.