Keplerian orbits can describe the motion of a negligible mass around a massive fixed central body, but they can also describe the motion of two bodies around their center of motion... with some constraints on their mass distributions.
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 that needs its own definition?
Each body has a significant, non- negligible size and could have a non-uniform, or potentially a non-spherically symmetric density distribution.