Test-time training (TTT) adapts an LLM during generation by reading and updating request-owned state, such as fast weights, low-rank deltas, or streaming learner state. This breaks batched LLM serving, which assumes shared static weights: serial execution is correct but slow, while naive batching can corrupt request state. We formulate this problem as read-write TTT serving and present RW-TTT, which tags each decode step with its owner, version, and READ/WRITE effect, batches only compatible phases, and commits updates only to the owner. On one GPU with eight fast-weight In-Place-TTT streams, RW-TTT reaches 274.61 aggregate tok/s, 9.31× over sequential serving and 3.44× over memory-matched independent replicas. It preserves behavior on RULER, a long-context benchmark, and passes owner/version checks.