Implants, implant systems, and methods for treatment of mitral valve regurgitation and other valve diseases generally include a coaptation assist body which remains within the blood flow path as the leaflets of the valve move, the valve bodies often being relatively thin, elongate (along the blood flow path), and/or conformable structures which extend laterally from commissure to commissure, allowing the native leaflets to engage and seal against the large, opposed surfaces on either side of the valve body during the heart cycle phase when the ventricle contracts to empty that chamber of blood, and allows blood to pass around the valve body so that blood flows from the atrium to the ventricle during the filling phase of the heart cycle. Separate deployment of independent anchors near each of the commissures may facilitate positioning and support of an exemplary triangular valve body, with a third anchor being deployed in the ventricle. An outer surface of the valve body may accommodate tissue ingrowth or endothelialization, while a fluid-absorbing matrix can swell after introduction into the heart. The valve body shape may be selected after an anchor has been deployed, and catheter-based deployment systems may have a desirable low profile.