Species afflicted by multiple threats are thought to face greater extinction risk. However, it is not known whether multiple threats operate antagonistically, additively, or synergistically, or whether they vary across different taxonomic and spatial scales. We addressed these questions by analyzing threats to 10,378 species in six vertebrate classes at global and regional spatial scales using network analysis. The total number of threats was a poor predictor of extinction risk, and particular combinations of threats did not predict extinction risk in the same way at different spatial scales. The exception was cartilaginous fishes, which faced increased extinction risk with increasing numbers of threats. Except for cartilaginous fishes, our findings indicate that species facing more threats than others do not face a higher risk of extinction and suggest that effective conservation will require more investment in identifying how threats and different ecosystem stressors operate together at local scales.