Keplerian orbits can describe the motion of a negligible mass around a massive fixed central body, but they also describe the motion of two bodies around their center of motion.
But which point within each body is the point that traces out it's orbit? And which two points define the distances used to determine the center of motion? Are they the center of mass, or the center of gravity, or in fact a different point?
Each body has a significant, non- negligible size and could have a non-uniform, or potentially a non-spherically symmetric density distribution.