The work presents a new signature scheme, called the multi-threshold signature, which generalizes the concept of multisignature and threshold signature. This scheme protects the anonymity of signers in a way the group signature does – in exceptional circumstances the identities of signers may be revealed. Due to the new party – completer, in our scheme the threshold size may vary together with the message to be signed. The presented scheme is based on the RSA signature standard, however other signature standards might be applied to it as well.