Large language models (LLMs) are increasingly deployed in teams, yet existing coordination approaches often occupy two extremes. Highly structured methods rely on fixed roles, pipelines, or task decompositions assigned a priori. In contrast, fully unstructured teams enable adaptability and exploration but suffer from inefficiencies such as error propagation, inter-agent conflicts, and wasted resources (measured in time, tokens, or file operations). We introduce Language Agent Teams for Task Evolution (LATTE), a framework for coordinating LLM teams inspired by distributed systems, where processors must operate under partial observability and communication constraints. In LATTE, a team of agents collaboratively construct and maintain a shared, evolving coordination graph which encodes sub-task dependencies, individual agent assignment, and the current state of sub-task progress. This protocol maintains consistency while empowering agents to dynamically allocate work, adapt coordination, and discover new tasks. Across multiple collaborative tasks and a variety of base models, we demonstrate how LATTE reduces token usage, wall-clock time, communication, and coordination failures (e.g. file conflicts and redundant outputs) while matching or exceeding the accuracy of standard designs including MetaGPT, decentralized teams, top-down Leader-Worker hierarchies, and static decompositions.