Parallel LLM test-time scaling techniques (e.g., best-of-$N$) require drawing $N>1$ sequences conditioned on the same input prompt. These methods boost accuracy while exploiting the computational efficiency of batching $N$ generations. However, each sequence in the batch is traditionally generated independently and hence does not reuse intermediate generations, computations, or observations from other sequences. In this paper, we propose LaneRoPE to enable coordination and collaboration among $N>1$ sequences at generation time. LaneRoPE involves two key ideas: (a) an inter-sequence attention mask to make sampling of sequences dependent on one another; and (b) a RoPE extension that injects positional information that captures relative positions between tokens, both within and outside a particular sequence. We evaluate our approach on mathematical reasoning tasks and find promising results: LaneRoPE enables collaboration among sequences, yielding additional accuracy gains under limited generated sequence length. Importantly, since LaneRoPE enables coordination with minimal changes to the underlying LLM architecture and introduces a negligible overhead at inference time, it is appealing to rapidly incorporate parallel reasoning into existing LLM inference pipelines.