We address control synthesis of stochastic discrete-time linear multi-agent systems under jointly chance-constrained collaborative signal temporal logic specifications in a distribution-free manner using available disturbance samples, which are partitioned into training and calibration sets. Leveraging linearity, we decompose each agent’s system into deterministic nominal and stochastic error parts, and design disturbance feedback controllers to bound the stochastic errors by solving a tractable optimization problem over the training data. We then quantify prediction regions (PRs) for the aggregate error trajectories corresponding to agent \textit{cliques}, involved in collaborative tasks, using conformal prediction and calibration data. This enables us to address the specified joint chance constraint via Lipschitz tightening and the computed PRs, and relax the centralized stochastic optimal control problem to a deterministic one, whose solution represents feedforward inputs. To enhance scalability, we decompose the deterministic problem into agent-level subproblems solved in an MPC fashion, yielding a distributed control policy. Finally, we present an illustrative example and a comparison with [1].