Bioimpedance imaging aims to generate a 3D map of the resistivity and permittivity of biological tissue from multiple impedance channels measured with electrodes applied to the skin. When the electrodes are distributed around the body (for example, by delineating a cross section of the chest or a limb), bioimpedance imaging is called electrical impedance tomography (EIT) and results in functional 2D images. Conventional EIT systems rely on individually cabling each electrode to master electronics in a star configuration. This approach works well for rack-mounted equipment; however, the bulkiness of the cabling is unsuitable for a wearable system. Previously presented cooperative sensors solve this cabling problem using active (dry) electrodes connected via a two-wire parallel bus. The bus can be implemented with two unshielded wires or even two conductive textile layers, thus replacing the cumbersome wiring of the conventional star arrangement. Prior research demonstrated cooperative sensors for measuring bioimpedances, successfully realizing a measurement reference signal, sensor synchronization, and data transfer though still relying on individual batteries to power the sensors. Subsequent research using cooperative sensors for biopotential measurements proposed a method to remove batteries from the sensors and have the central unit supply power over the two-wire bus. Building from our previous research, this paper presents the application of this method to the measurement of bioimpedances. Two different approaches are discussed, one using discrete, commercially available components, and the other with an application-specific integrated circuit (ASIC). The initial experimental results reveal that both approaches are feasible, but the ASIC approach offers advantages for medical safety, as well as lower power consumption and a smaller size.