CBASS is a common anti-phage immune system that uses cyclic oligonucleotide signals to activate effectors and limit phage replication. In turn, phages encode anti-CBASS (Acb) proteins. We recently uncovered a widespread phage anti-CBASS protein Acb2 that acts as a "sponge" by forming a hexamer complex with three cGAMP molecules. Here, we identified that Acb2 binds and sequesters many CBASS and cGAS-produced cyclic dinucleotides in vitro and inhibits cGAMP-mediated STING activity in human cells. Surprisingly, Acb2 also binds CBASS cyclic trinucleotides 3'3'3'-cyclic AMP-AMP-AMP (cA3) and 3'3'3'-cAAG with high affinity. Structural characterization identified a distinct binding pocket within the Acb2 hexamer that binds two cyclic trinucleotide molecules and another binding pocket that binds to cyclic dinucleotides. Binding in one pocket does not allosterically alter the other, such that one Acb2 hexamer can simultaneously bind two cyclic trinucleotides and three cyclic dinucleotides. Phage-encoded Acb2 provides protection from Type III-C CBASS that uses cA3 signaling molecules in vivo and blocks cA3-mediated activation of the endonuclease effector in vitro. Altogether, Acb2 sequesters nearly all known CBASS signaling molecules through two distinct binding pockets and therefore serves as a broad-spectrum inhibitor of cGAS-based immunity.