We show the viability of tackling misuses of large language models beyond the identification of machine-generated text. While existing zero-bit watermark methods focus on detection only, some malicious misuses demand tracing the adversary user for counteracting them. To address this, we propose Multi-bit Watermark via Position Allocation, embedding traceable multi-bit information during language model generation. Through allocating tokens onto different parts of the messages, we embed longer messages in high corruption settings without added latency. By independently embedding sub-units of messages, the proposed method outperforms the existing works in terms of robustness and latency. Leveraging the benefits of zero-bit watermarking, our method enables robust extraction of the watermark without any model access, embedding and extraction of long messages ($\geq$ 32-bit) without finetuning, and maintaining text quality, while allowing zero-bit detection all at the same time. Code is released here: https://github.com/bangawayoo/mb-lm-watermarking