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Great idea but you are assuming a lot. You are assuming that the SEC WANTS to stabilize the ACC.
I think all signs would be indicative of the SEC wanting to have the opposite effect on the stability of the ACC... they know at some point they want to go east (to get to 16) and to do that, they are going to want ACC schools from the mid-atlantic region.
I think that is why the SEC arranged the Bowl game with the Big XII (which was near extinction, on 2 occasions over the last 2 years), instead of a growing ACC.
Because outside of Texas and Oklahoma, how many tradition rich programs exist in the Big XII, especially if you look at the history of college football, prior to 2000.
It's all cyclical. Compare Texas/OU to Miami/FSU in the 90's. Heck, even do it with the same teams from the 80's (OU started to dip in the late 80's and FSU started to rise at about the same time, around '87, I believe).
Then, look at the history of the ACC vs. Big XII's other members, say, prior to 2000. Look at national championships and 8 win seasons (I say 8 because it used to be that they played only 11 game schedules).
Once one makes those comparisons, they see that the long-term tradition, lies within the ACC and not the Big XII. Remember, we are talking about both conferences current members (including Pitt and Syarcuse, which will probably be in the ACC, starting next season).
2 years, 6 months ago on Push Begins For Regular-Season Big 12-SEC Games, But SEC-ACC Games May Make More Sense