Promising multifunctional magnetoresponsive effects such as magnetoresistance, magnetostrain, and the magnetocaloric effect have recently been extensively studied in Ni-Mn-based metamagnetic shape memory alloys, but large reversible magnetoresponsive effects are usually obtained under high magnetic fields, which is an obstacle for practical applications. Here, through manipulating magnetostructural transition, we achieved large reversible magnetoresponsive effects under a relatively low magnetic field of 3 T in a Ni-Co-Mn-In alloy. By systematically tuning the Mn/In ratio and Co substitution, an optimum composition Ni49Co3Mn34In14 with a low thermal hysteresis (8 K), a narrow transformation interval (7 K) and a high sensitivity of transformation temperature to field change (6KT-1), was obtained. Good geometric compatibility between austenite and martensite was revealed by in situ synchrotron high-energy x-ray diffraction experiment, which accounts for the low hysteresis and narrow transformation interval. A reversible transformation between pure austenite and pure martensite is induced by a relatively low field of 3 T, which was directly evidenced by in situ neutron diffraction experiments. As a result, a large reversible magnetocaloric effect with entropy change of 16.5Jkg-1K-1, a large reversible magnetostrain of 0.26%, and a large reversible magnetoresistance of 60%, under a relatively low field of 3 T, were simultaneously achieved. These reversible magnetoresponsive effects are comparable to the maximum reversible values obtained under high fields in other Ni-Mn-based alloys, but the magnetic field we applied is much lower. This study may guide the design of metamagnetic shape memory alloys with low-field-induced magnetoresponsive properties for magnetic refrigeration, magnetic sensing, and magnetic recording applications.