Sanitizable signatures allow a signer of a message to give one specific receiver, called a sanitizer, the power to modify some designated parts of the signed message. Most of the existing constructions consider one single signer giving such a possibility to one single sanitizer. In this paper, we formalize the concept with n signers and m sanitizers, taking into account recent models (for 1 signer and 1 sanitizer) on the subject. We next give a generic construction based on the use of both group signatures and a new cryptographic building block, called a trapdoor or proof, that may be of independent interest.