General idea; generalise the Schnorr scriptless script atomic swap of A Poelstra to multiple parties.
We consider 3-party case with trivial generalisation. Parties are Alice, Bob, Charlie, A, B, C. Payment destinations are D_x. Transactions are TX_x. Adaptor signature secrets are t_x (scalar), T_x (point). Signatures are "sigma", adaptor signatures will be marked with '.