Polycomb repression complex 1 (PRC1) is a multiprotein assembly that regulates transcription. The Polycomb group ring finger 1 protein (PCGF1) is central in the assembly of the noncanonical PRC1 variant called PRC1.1 through its direct interaction with BCOR (BCL-6-interacting corepressor) or its paralog, BCOR-like 1 (BCORL1). Previous structural studies revealed that the C-terminal PUFD domain of BCORL1 is necessary and sufficient to heterodimerize with the RAWUL domain of PCGF1 and, together, form a new protein-protein binding interface that associates with the histone demethylase KDM2B. Here, we show that the PUFD of BCOR and BCORL1 differ in their abilities to assemble with KDM2B. Unlike BCORL1, the PUFD of BCOR alone does not stably assemble with KDM2B. Rather, additional residues N-terminal to the BCOR PUFD are necessary for stable association. Nuclear magnetic resonance (NMR) structure determination and 15N T2 relaxation time measurements of the BCOR PUFD alone indicate that the termini of the BCOR PUFD, which are critical for binding PCGF1 and KDM2B, are disordered. This suggests a hierarchical mode of assembly whereby BCOR PUFD termini become structurally ordered upon binding PCGF1, which then allows stable association with KDM2B. Notably, BCOR internal tandem duplications (ITDs) leading to pediatric kidney and brain tumors map to the PUFD termini. Binding studies with the BCOR ITD indicate the ITD would disrupt PRC1.1 assembly, suggesting loss of the ability to assemble PRC1.1 is a critical molecular event driving tumorigenesis.