The wide ranging magnetic behavior in intermetallic compounds continues to attract broad interest. Effective control of their magnetic properties is of great importance for fundamental research and potential applications. In this work the structural and magnetic properties of TbCo2Mnx compounds are studied by a combination of temperature dependent synchrotron x-ray diffraction, neutron powder diffraction, specific heat, and magnetic measurements. Magnetization measurements show that the addition of Mn can modify the magnetic behavior significantly: first, the magnetic transition temperatures increase from ∼227 K to 332 K with x = 0.0 to 0.3; secondly, the nature of the magnetic transitions change from the first order to second order, as identified by three methods (Banerjee criterion, master curves of magnetic entropy changes, and detailed crystal structure analysis through neutron diffraction). Both synchrotron x-ray diffraction and neutron diffraction confirm that a structural transition, from cubic Fd3¯m to rhombohedral R3¯m on cooling, occurred accompanying the magnetic transition. To further clarify the nature of the second order magnetic phase transitions, we have carried out a detailed critical exponent analysis. The derived critical exponents are close to the theoretical prediction from the mean-field model, indicating the magnetic interactions are long range. This work benefits our general understanding of magnetic interactions in intermetallic compounds and provides guidance to design a functional magnetic material for room temperature magnetic devices.