I don't agree with Sam Gerstenzang's answer. All the factors he talks about come later. Elitism has almost nothing to do with organizational design, and everything to do with whether you have the right raw material for a powerful origin myth to form, and enough money for that raw material to do weird things.

The signature aspects of institutional design that come later follow via consistency with the origin myth. You CANNOT make general statements like "avoid varsity sports in the beginning." What if your origin myth IS a bunch of inner-city kids who failed to get basketball scholarships, who form a fantastic basketball team and beat the crap out of the top university team in an exhibition match, prompting a famous black entrepreneur to endow a new university just to give them a home?

So what's the right raw material for a founding myth? Look at some examples (boldface emphasis mine):

Harvard: http://news.harvard.edu/guide/co...

Harvard is the oldest institution of higher education in the United

states, established in 1636 by vote of the Great and General Court of

the Massachusetts Bay Colony. It was named after the College's first

benefactor, the young minister John Harvard of Charlestown, who upon his

death in 1638 left his library and half his estate to the institution. A

statue of John Harvard stands today in front of University Hall in

Harvard Yard, and is perhaps the University's best known landmark.

Oxford: http://www.ox.ac.uk/about_the_un...

As the oldest university in the English-speaking world, Oxford is a

unique and historic institution. There is no clear date of foundation,

but teaching existed at Oxford in some form in 1096 and developed

rapidly from 1167, when Henry II banned English students from attending

the University of Paris.

MIT: http://en.wikipedia.org/wiki/His...

With the charter approved, Rogers began raising funds, developing a

curriculum and looking for a suitable location. The Rogers Plan, as it

came to be known, was rooted in three principles: the educational value

of useful knowledge, the necessity of “learning by doing,” and

integrating a professional and liberal arts education at the

undergraduate level.MIT was a pioneer in the use of laboratory instruction. Its founding philosophy is "the teaching, not of the manipulations and minute details of the arts, which can be done only in the workshop, but

the inculcation of all the scientific principles which form the basis

and explanation of them;"

I'll leave you to search "History of X" (substitute your favorite elite university).

The pattern I want to highlight is that origin myths form around an "exceptionalism" narrative. These form around unusual people, unusual events in history or through opposition of established ideas about how to teach. Basically, without a "we're different because _________" angle you can't differentiate, and without differentiation, you cannot get to elite.

If there is no exceptionalism narrative, you can build all the system-process scaffolding you want. You won't get to "elite."

Think of it as the random particle of dust around which a very regular crystal can form. Or the sand particle around which a pearl forms in an oyster. In both cases, the original stimulus MUST be weird/awkward. The grain of sand "irritates" the oyster into creating a pearl around it. The dust particle disturbs the symmetries of a supersaturated solution. If you cool extremely pure solutions very very slowly, you can actually supercool them without causing freezing... for the same reason, very pure water may superheat without boiling in the microwave, and explode the moment you open the door and disturb it. Which is why you use the trick of putting in a wooden skewer or something in a carafe of water to heat. It disturbs the water enough that boiling begins at 100 degrees.

The process is very similar in some ways to the establishment of new brands, but is much broader because universities are such fundamental institutions that span so many aspects of civil society.