We introduce Multimodal Private Signature (MPS) - an anonymous signature system that offers a novel accountability feature: it allows a designated opening authority to learn some partial information op about the signer’s identity id, and nothing beyond. Such partial information can flexibly be defined as op= id (as in group signatures), or as op= 0 (like in ring signatures), or more generally, as op= Gj(id), where Gj(· ) is a certain disclosing function. Importantly, the value of op is known in advance by the signer, and hence, the latter can decide whether she/he wants to disclose that piece of information. The concept of MPS significantly generalizes the notion of tracing in traditional anonymity-oriented signature primitives, and can enable various new and appealing privacy-preserving applications. We formalize the definitions and security requirements for MPS. We next present a generic construction to demonstrate the feasibility of designing MPS in a modular manner and from commonly used cryptographic building blocks (ordinary signatures, public-key encryption and NIZKs). We also provide an efficient construction in the standard model based on pairings, and a lattice-based construction in the random oracle model.