We propose a novel high-force/high-precision interaction control framework of a dual-arm robot system on a flexible base, with one arm holding, or making contact with, a supporting surface, while the other arm can exert any arbitrary wrench in a certain polytope through a desired pose against environments or objects. Our proposed framework can achieve high-force/precision tasks by utilizing the supporting surface just as we humans do while taking into account various important constraints (e.g., system stability, joint angle/torque limits, friction-cone constraint, etc.) and the passive compliance of the flexible base. We first design the control as a combination of: 1) nominal control; 2) active stiffness control; and 3) feedback wrench control. We then sequentially perform optimizations of the nominal configuration (and its related wrenches) and the active stiffness control gain. We also design the proportional–integral type feedback wrench control to improve the robustness and precision of the control. The key theoretical enabler for our framework is a novel stiffness analysis of the dual-arm system with flexibility, which, when combined with certain constraints, provides some peculiar relations, that can effectively be used to significantly simplify the optimization problem-solving and to facilitate the feedback wrench control design by manifesting the compliance relation at the interaction port. The efficacy of the theory is then validated and demonstrated through simulations and experiments.