Robotic hand engineers usually focus on finger capabilities, often disregarding the palm contribution. Inspired by human anatomy, this paper explores the advantages of including a flexible concave palm into the design of a robotic hand actuated by soft synergies. We analyse how the inclusion of an articulated palm improves finger workspace and manipulability. We propose a mechanical design of a modular palm with two elastic rolling-contact palmar joints, that can be integrated on the Pisa/IIT SoftHand, without introducing additional motors. With this prototype, we evaluate experimentally the grasping capabilities of a robotic palm. We compare its performance to that of the same robotic hand with the palm fixed, and to that of a human hand. To assess the effective grasp quality achieved by the three systems, we measure the contact area using paint-transfer patterns in different grasping actions. Preliminary grasping experiments show a closer resemblance of the soft-palm robotic hand to the human hand. Results evidence a higher adaptive capability and a larger involvement of all fingers in grasping.