We present a unified framework for grasp planning and in-hand grasp adaptation using visual, tactile, and proprioceptive feedback. The main objective of the proposed framework is to enable fingertip grasping by addressing problems of changed weight of the object, slippage, and external disturbances. For this purpose we introduce the Hierarchical Fingertip Space as a representation enabling optimization for both efficient grasp synthesis and online finger gaiting. Grasp synthesis is followed by a grasp adaptation step that consists of both grasp force adaptation through impedance control and regrasping/finger gaiting when the former is not sufficient. Experimental evaluation is conducted on an Allegro hand mounted on a Kuka LWR arm.