An intrinsically switchable ferroelectric barium strontium titanate (BST) stacked crystal filter (SCF) is presented for the first time. A single pole BST SCF is designed for a second overtone (mode 2) operating at 3.6 GHz. The fabricated device provides a high out-of-band rejection and off state isolation of more than 25 dB, which is a >10 dB improvement over a single stage BST ladder-type structure with similar specifications. The measured insertion loss and 3-dB fractional bandwidth (FBW) are shown to be 3 dB and 4.3%, respectively. These metrics are obtained for a single pole SCF, which occupies a footprint of less than 400 (µm)², significantly more compact than traditional acoustic filters.