The underactuation of conventional aerial vehicles limits their ability to independently control position and attitude, motivating the use of overactuated designs such as tilt-rotor quadrotors. Existing works on tilt-rotor quadrotors primarily focus on determining the minimum thrust-to-weight ratio required for hovering at arbitrary orientations. However, they do not address the maximum allowable attitude range within which independent control is feasible given specific thrust constraints. In this work, we investigate the feasible attitude range within which a tilt-rotor quadrotor can maintain independent control, given rotor thrust limits. First, we formulate the thrust constraints as convex functions and solve them using convex optimization techniques to identify feasible sets. To determine the maximum attitude that allows for independent control under thrust constraints, we pose a nonconvex optimization problem and employ a successive convex approximation (SCA) technique to compute a optimal solution, which corresponds to the optimal solution of the original nonconvex problem. Given the maximum attitude limits, we then compute the minimum thrust required per rotor to achieve independent control. Furthermore, we determine the maximum allowable disturbance magnitude that the tilt-rotor quadrotor can handle while retaining independent control. The study results are verified through processor-in-the-loop (PIL) simulations and outdoor hardware experiments on a tilt-rotor quadrotor. An illustrative video showing both the PIL simulation and hardware experimental results can be found at: https://youtu.be/6qjc9_KtACM Note to Practitioners—This paper is motivated by the potential application of tilt-quadrotors in inspection, search and rescue, and aerial manipulation, owing to their ability to perform agile maneuvers in confined environments. However, ensuring independent control of both position and attitude across all orientations remains a practical challenge, primarily...