The beyond unforgeability features formalize additional security properties for signature schemes. We develop a general framework of binding properties for signature schemes that encompasses existing beyond unforgeability features and reveals new notions. Furthermore, we give new results regarding various transforms: We show that the transform by Cremers et al. (SP’21) achieves all of our security notions; we give a modified definition of so-called weak keys, and show that the Pornin–Stern transform (ACNS’05) also achieves all notions if there are no weak keys. Finally, we connect our framework to unforgeability notions.