In this paper, we investigate the task-space adaptive control problem for free-floating space manipulators with uncertain kinematics and dynamics and with an unmodifiable inner joint control loop. The existence of an unmodifiable inner joint control loop makes most torque-based control algorithms in the literature inapplicable. We propose a dynamic modularity (DM) approach to resolve this problem, and this is hopeful for bridging the potential gap between the advanced control theory for (free-floating) space manipulators and practical engineering applications. Adaptive outer loop controllers are developed and shown to be able to guarantee the convergence of the task-space tracking errors. The performance of the proposed DM approach is shown by a numerical simulation.