Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually disjoint Euclidean Steiner trees that avoid clutter and overlapping with obstacles in the plane, which is significant to model the decentralized and the multipoint coordination of agents in constrained 2D domains. Our computational experiments using arbitrary obstacle configuration with convex and non-convex geometries show the feasibility and the attractive performance when computing multiple obstacle-avoiding Steiner trees in the plane. Our results offer the mechanisms to elucidate new operators for obstacle-avoiding Steiner trees.