Deploying companion robots for assisting humans requires safe and robust interaction with the environment, both in terms of mobility and object manipulation. To extend a robot's workspace, we are here concerned with multifloor operation and staircase traversal, as a building block for the development of object fetching services. In this article, we advocate a lifelong learning treatment of this problem within a reinforcement learning (RL) framework. In view of sparse earlier work for the scenario of interest, we hereby identify relevant methodological aspects and report our preliminary developments.