None! 
(Actually, not really joking - the Ivy League has nothing to gain, nor does society. The current system is perfectly fine, where a bunch of “nerdy” kids have sports teams with accomplished athletes, who low-stakes compete amongst a few local peers – but the schools are defined by academics, not primarily by sports programs.)
They already experimented with that, by broadening up-state…
I’m waiting for that ACC announcement.
Princeton might take issue with this 
That never stopped anyone…
Adding schools might ease some of the admission noise… maybe.
By design, they are free to prevent that from ever happening.
You misunderstand. Some Princeton sports have a fierce rivalry with Harvard, others with Yale. Your design is based on the premise the Harvard vs Yale is the prominent and only relevant rivalry.
Understood.
Geographically… I had no choice. I guess I could swap North/South for East/West…and swap Williams and Yale.
You know what…you talked me into it.
2 new schools in each division… home and home for Yale/Harvard…and Princeton can go back and forth between the two for championships.
UofT and McGill don’t have athletic recruiting (or at least not the way it’s done in the US). I doubt their athletics are at the level of D1 sports and that’s the way Canadian’s like it. Admission to university is based on academics. If you want to play sports that’s fine, but it’s not going to get you an admit.
Sure so long as by "Ivy League’ you mean Harvard, Yale, Princeton, and maybe Columbia.
Nope. I specifically mean all of the eight institutions. Again, being in the “Ivy League” has an inestimable value to it, and adding more colleges will, IMHO, negatively affect that.
Remember also the world-class graduate programs that most have (e.g., Penn/Wharton, Cornell - law, medicine, business, etc.)
Even for the alleged “lesser” Ivies (to the extent there is such a thing), the Ivy League branding greatly helps them.
That’s precisely why I don’t see the Ivy League schools letting any other school in.
And upthread, we’re talking about Harvard/Yale/perhaps Princeton as the sporting greats of this league. Let’s not forget that Princeton has made the NCAA Men’s Basketball Sweet 16 twice (including this year), Penn went to the Final Four in 1979, and I believe Dartmouth went to the Final 2 (or whatever it was called back then) during WW II. AFAIK, those are the only three schools to advance this far.
For sports, it ain’t just Harvard and Yale.
On CC, we’ve already expanded the Ivy League to include S & M (HYPSM), so we might as well make it official and admit Stanford and Michigan. 
The majority of the international students I come across looking to apply to the Ivy League frequently use the term euphemistically to mean “top university” which to them is primarily HYPSM + Columbia, and are unfamiliar with the “lesser Ivy’s”. To be fair though the most of them are targeting STEM graduate programs specifically so that may be why.
Except that the “M” in HYPSM is MIT, not Michigan.
If you are looking for a 4 team expansion, I would go with Georgetown, JHU, CMU and UChicago. It would increase the footprint into cities that have good concentrations of Ivy grads.
That’s a common misconception.
Moreover, St. Louisans know that MIT stands for
Meramec
In
Town
(Meramec is a local community college).
Tufts is athletically strong enough and it is almost too large to stay in the NESCAC League. They need to add women’s hockey.
Colgate could be an interesting choice.
A school, with permission (often from a grandfather clause) can ‘play up’ 2 teams, one men’s and one women’s. I don’t believe they can play up in football or basketball. D1 schools cannot ‘play down’ but some do have club teams rather than drop the sport.
Note that there are a variety of different degrees of athletic competitiveness within Div I or within Div III. Being able to play on Div I level in some sports does not mean competitive within Ivy League conference. In the most recent Director’s Cup final standings, the highest ranked college overall in Div I athletics was Stanford, followed by Texas, Ohio State, Virginia, and Florida. The median rank for Ivy League colleges was ~70th, which is top 20% of Div I or so. Ivy League colleges have high national rankings in several Div I sports each year, which is the basis of the Director’s Cup standings. Sometimes they win national championships.
However, I’d expect the sports performance that matters most for Ivy League colleges are football, men’s basketball, and ice hockey; which have a good amount of interest from students, alumni, and the general population as a whole. Ivy League colleges do better than many expect in these sports, even compared to other colleges with similar Director’s Cup rankings.
For example, Georgetown was ranked #67 in the most recent Director’s Cup, placing almost directly on the Ivy League median, yet Georgetown football is not competitive with Ivy League level. Every time Georgetown and Harvard have played a football game, Georgetown lost badly. The most recent game was 44 to 9. They have had losses as bad as 45 to 0 before. I don’t see Georgetown football improving, if Georgetown eliminates their football scholarships, per Ivy League rules.
I am not sure this is true. Certainly not football.
Soccer, Field Hockey and Lacrosse are huge. But they also care about Crew, Cross-country, Swimming, Fencing….
I suggest maybe they add Oregon State and Washington State…they’re available.