Recent interest in mobile manipulation has resulted in a wide range of new robot designs. A large family of these designs focuses on modular platforms that combine existing mobile bases with static manipulator arms. They combine these modules by mounting the arm in a tabletop configuration. However, the operating workspaces and heights for common mobile manipulation tasks, such as opening articulated objects, significantly differ from tabletop manipulation tasks. As a result, these standard arm mounting configurations can result in kinematics with restricted joint ranges and motions. To address these problems, we present the first Concurrent Design approach for mobile manipulators to optimize key arm-mounting parameters. Our approach directly targets task performance across representative household tasks by training a powerful multitask-capable reinforcement learning policy in an inner loop while optimizing over a distribution of design configurations guided by Bayesian Optimization and HyperBand (BOHB) in an outer loop. This results in novel designs that significantly improve performance across both seen and unseen test tasks, and outperform designs generated by heuristic-based performance indices that are cheaper to evaluate but only weakly correlated with the motions of interest. We evaluate the physical feasibility of the resulting designs and show that the are practical and remain modular, affordable, and compatible with existing commercial components.We open-source the approach and generated designs to facilitate further improvements of these platforms.