Traceable ring signatures enhance ring signatures by adding an accountability layer. Specifically, if a party signs two different messages within the protocol, their identity is revealed. Another desirable feature is extendability. In particular, extendable threshold ring signatures ( \(\textsf{ETRS}\) ) allow to non-interactively update already finalized signatures by enlarging the ring or the set of signers. Combining traceability and extendability in a single scheme is unexplored and would offer a new tool for privacy-preserving voting schemes in scenarios where the voters are not known in advance. In this paper, we show how to reconcile both properties by introducing and constructing a new cryptographic primitive called Tetris. Notably, our Tetris construction simultaneously achieves a strong flavor of anonymity and linear-size signatures, which is the main technical challenge in existing techniques. To solve this challenge, we develop a new approach to traceability that leads to several conceptual and technical contributions. Among those, we introduce and construct, based on Groth-Sahai proofs, extendable shuffle arguments that can be non-interactively updated by several provers.