When planning functional grasps of tools, right-handed individuals (dextrals) show mostly left-lateralized neural activity in the praxis representation network (PRN), regardless of the used hand. Here we studied whether or not similar cerebral asymmetries are evident in non-righthanded individuals (adextrals). Sixty two participants, 28 righthanders and 34 non-righthanders (21 lefthanders, 13 mixedhanders), planned functional grasps of tools vs. grasps of control objects, and subsequently performed their pantomimed executions, in an event-related functional magnetic resonance imaging (fMRI) project. Both hands were tested, separately in two different sessions, counterbalanced across participants. After accounting for non-functional components of the prospective grasp, planning functional grasps of tools was associated with greater engagement of the same, left-hemisphere occipito-temporal, parietal and frontal areas of PRN, regardless of hand and handedness. Only when the analyses involved signal changes referenced to resting baseline intervals, differences between adextrals and dextrals emerged. Whereas in the left hemisphere the neural activity was equivalent in both groups (except for the occipito-temporo-parietal junction), its increases in the right occipito-temporal cortex, medial intraparietal sulcus (area MIP), the supramarginal gyrus (area PFt/PF), and middle frontal gyrus (area p9-46v) were significantly greater in adextrals. The inverse contrast was empty. Notably, when individuals with atypical and typical hemispheric phenotypes were directly compared, planning functional (vs. control) grasps invoked, instead, significant clusters located nearly exclusively in the left hemisphere of the typical phenotype. Previous studies interpret similar right-sided vs. left-sided increases in neural activity for skilled actions as handedness dependent, i.e., located in the hemisphere dominant for manual skills. Yet, none of the effects observed here can be purely handedness dependent because there were mixed-handed individuals among adextrals, and numerous mixed-handed and left-handed individuals possess the typical phenotype. Thus, our results clearly show that hand dominance has limited power in driving the cerebral organization of motor cognitive functions.