Dexterous robot hand teleoperation allows for long-range transfer of human manipulation expertise, and could simultaneously provide a way for humans to teach these skills to robots. However, current methods struggle to reproduce the functional workspace of the human hand, often limiting them to simple grasping tasks. We present a novel method for finger-gaited manipulation with multi-fingered robot hands. Our method provides the operator enhanced flexibility in making contacts by expanding the reachable workspace of the robot hand through residual Gaussian Process learning. We also assist the operator in maintaining stable contacts with the object by allowing them to constrain fingertips of the hand to move in concert. Extensive quantitative evaluations show that our method significantly increases the reachable workspace of the robot hand and enables the completion of novel dexterous finger gaiting tasks. Project website: respilot-hri.github.io.