Is there an upper limit on the coordination number of a coordination compound?
I don't see why not. It is a matter of having


enough of an interaction between the center and the ligands, usually in the form of donor/acceptor orbital pairs, and
enough space around the coordination center.


These go hand-in-hand, as any atom that will have enough electrons to donate to ligands will also most likely have a larger atomic radius than a first-row transition metal like iron.

For example, here is a thorium complex that has CN = 15 in its crystal structure and CN = 16 in an isolated gas-phase density functional calculation:



Daly, Scott R.; Piccoli, Paula M. B.; Schultz, Arthur J.; Todorova, Tanya K.; Gagliardi, Laura; Girolami, Gregory S. Synthesis and Properties of a Fifteen-Coordinate Complex: The Thorium Aminodiboronate $\ce{[Th(H3BNMe2BH3)4]}$. Angew. Chem. Int. Ed. 2010, 49, 3379-3381, DOI: 10.1002/anie.200905797