Co3In2S2 is a shandite phase closely related to the ferromagnetic Weyl semimetal Co3Sn2S2 and contains Co atoms on an ideal kagome net. Elemental substitutions in Co3Sn2S2 have been shown to invariably suppress its magnetism, and it remains a rare example of a shandite phase with magnetic order. Here, we report a new magnetic shandite compound discovered by substituting Fe into Co3In2S2. Single crystals of (Co1–xFex)3In2S2 were grown, and neutron diffraction, ac and dc magnetization, and heat capacity measurements reveal long-range antiferromagnetic order with an interesting noncollinear structure and transition temperatures from 11 to 17 K. Partially substituting Fe for Co was inspired by calculated electronic structures, which suggest that Co3In2S2 is near a magnetic instability and shows a peak in the density of states that can be approached by hole doping. While the focus of the present work is primarily on magnetism, there is a nodal ring below the Fermi energy in Co3In2S2 that may also provide interest from a topological perspective. Potentially related to this, we find large, linear, nonsaturating magnetoresistance in this compound. This work expands the scope of magnetic topological materials among shandites and motivates similar chemical manipulation studies to reveal hidden magnetic instabilities in this important family and other topological systems.