The next-closest companion, the magnitude 11.59 WDS 07291+3147 C, had a much larger separation of 211.6 arcseconds in 1886. However, this separation increased by 10 arcseconds by 2001, indicating that it is a background star that is unrelated to Rho Geminorum. Correcting for Rho Geminorum A's proper motion, this star's proper motion is RA = -19 mas/yr and Dec = -55 mas/yr. This is a modestly large value, consistent with a distance of a few hundred light-years. WDS 07291+3147 C is itself listed as having a companion, the magnitude 13.20 WDS 07291+3147 D. Relative to WDS 07291+3147 C its separation has remained at about 100 arcseconds between 1909 and 2001, indicating similar proper motion. While this would indicate that the two stars are bound, at a large distance this separation would indicate a separation of at least several thousand AU and their mutual separation has not been entirely consistent (the position angle has increased from 267 to 270°, and the separation has decreased from 104.1 to 102.3 arcseconds). It is therefore possible that the two background stars are bound, but it is not certain.
