Current research on robotic dexterous hands mainly focuses on designing new finger and palm structures, as well as developing smarter control algorithms. Although the dimensional synthesis of dexterous hands with traditional rigid palms has been carried out, research on the dimensional synthesis of dexterous hands with metamorphic palms remains insufficient. This study investigated the dimensional synthesis of a palm of a novel metamorphic multi-fingered hand, and explored the geometric design for maximizing the precision manipulation workspace. Different indexes were used to value the workspace of the metamorphic hand, and the best proportions between the five links of the palm to obtain the optimal workspace of the metamorphic hand were explored. Based on the fixed total length of the palm member, four nondimensional design parameters that determine the size of the palm were introduced; through the discretization method, the influence of the four design parameters on the workspace of the metamorphic hand with full-actuated fingers and under-actuated fingers was analyzed. Based on the analysis of the metamorphic multi-fingered hand, the symmetrical structure of the palm was designed, resulting in the largest workspace of the multi-fingered hand, and proved that the metamorphic palm has a massive upgrade for the workspace of underactuated fingers. This research contributed to the dimensional synthesis of metamorphic dexterous hands, with practical significance for the design and optimization of novel metamorphic hands.