From application point of view, offstoichiometric Ni2MnGa is of interest and therefore many studies on offstoichiometric Ni2MnGa have been reported. Special focus has been paid on Ni rich Ni2MnGa, where substitution of Ni for Mn results in an increase in TM and decrease of TC, resulting in an overlap of the two transitions for certain Mn concentration [1]. As mentioned earlier, the martensitic transition is a first order transition where as the transition at TC from ferromagnetic order to a paramagnetic order is a second order transition. It is found that the overlap of TM and TC results in a first order magnetostructural transition from the paramagnetic cubic phase to ferromagnetic martensitic phase. Recent investigations show that this first order magnetostructural transition, due to the overlap of TM and TC, results in a fairly large magnetic entropy change, SM, in offstoichiometric Ni2MnGa. In this paper we present a study on the gradual overlap of the first order and second order phase transitions and the related magnetic entropy changes of polycrystalline Ni2+xMn1-xGa (x = 0.16, 0.17, 0.18, 0.19, 0.20). Ingots of approximately 5gm of polycrystalline Ni2+xMn1-xGa (x = 0.17, 0.18, 0.19, 0.20) were fabricated by conventional arc melting in an argon atmosphere using Ni, Mn, and Ga or 4N purity. The samples were annealed in vacuum for 144 hours at 800°C, and slowly cooled down to room temperature.