Illinois is 6-7 since 1990 with wins in 1990, 1992, 1994, 1999, 2001, and 2007. I get that the Illini owned Cooper early on, winning 5 straight from 1988-1992 and taking another in 1994, but even if we look at 1995 and beyond, the Illini still tie for the lead with 3.
MSU is 3-7 but with painful steals against two of our most talented teams (1998, 2011, and 2015)
Wisconsin is 3-7 catching the Buckeyes in the Horseshoe in some down years while the Badgers were up (1999, 2001, and 2004).
Michigan is 3-11-1 (1990, 1996, and 2000)
Penn State is 2-11 (2008 and 2011)
Iowa is 1-7 with a win in 1991
Minnesota is 1-10 with their win on Homecoming in 2000
Purdue is 0-8
NW is 0-9
IU is 0-13
The current Big XII schools are 2-2 (Texas in 2005 and OU in 2017)
The PAC 12 is 2-11 (USC being 2-0 with wins in 1990 and 2009)
The current ACC schools are 1-5 (VT in 2014)
The current SEC schools are 0-1 with only Mizzou playing the Buckeyes in 1998