score:5
As far as I can tell, there seems to be no IATA or ICAO rule regarding the maximum number of codeshares a flight may be marketed under. I imagine there must be a technological limitation at some point, but having seven or eight codeshares is not terribly uncommon, and flights with a dozen or more have been reported in discussions at FlyerTalk and at Airliners.Net, for example.
There is probably a way for someone with GDS access to deduce the most-codeshared current flight. Flight numbers and codeshares change frequently, so that would be the only definitive way, and only for a period of weeks at best. But the FT thread suggest SYD/MEL-AUH; today's schedule on FlightStats.com indeed turns up two Etihad flights with 14 and 12 codeshares respectively, more than any other city pair I tried:
Etihad EY 455 SYD-AUH = A3 1915, AB 4071, AF 3821, AZ 3925, B2 355, EI 8055, HM 5105, JU 8583, KL 3939, KM 2122, ME 6637, NZ 4255, S7 4606, VA 7093
Etihad EY 461 MEL-AUH = AF 3823, A3 1911, AB 4055, AZ 3923, B2 361, HM 5101, JU 8581, KM 2158, NZ 4261, KL 3941, ME 6639, VA 7095
The best I could do in the domestic US market was a 10-codeshare ORD-ATL Republic flight: