That would be called a franchise. Other repeatable business models generally aren't scalable, or are by necessity local... so they're destined to be small businesses.
Franchise to me implies licensing branding and/or materials from a franchiser, and while that certainly covers one case, it is not all-inclusive of possible answers to the question.
If you change the definition from "find" to "find and prove" it holds quite nicely (but doesn't sound as good). This works on the theory that there are no applicable, proven, scalable, repeatable business models. (Due to the presence of established competition)
Models proven to be un-scalable and or un-repeatable is trivially possible.
Models which are scalable and repeatable but un-proven can exist, the company will be executing the business model and in that they will be demonstrating the viability of it assuming the company will lives long enough that this is possible. (Good ideas can still fail if they hit an early setback and don't recover)
If the model is proven to be scalable and repeatable then there has to be someone who proved it to be so (And given the quality of the business model and its lack of glaring flaws they will still be around). With this in mind the original proving company is first to market and likely has a huge advantage, so unless the original product is markedly worse than the new one the model is not scalable and repeatable due to competition (contradiction)
My example is my own company, slicehost. I don't believe that we needed to find and/or prove the business model. It was a simple hosting model, we just thought we could do it more efficiently. Granted along the way new models arose from the automation inherent to the efficiency, but we already had profitability and traction at that point, it wasn't a requisite to 'making it'.
Now is efficiency gain (or conversely quality improvement) alone enough to make it qualify as a brand new business model? I'd argue that it is not.
My anecdotal support for my theory here is that we felt initially that we were taking very little risk in starting the business. It was clear and obvious to us that we could survive on the implied margins of other providers and acquiring customers in hosting at that point in time was relatively non-competitive.
I think Blank's distinction is helpful, in emphasizing that the term 'start-up' implies more model uncertainty and innovation.
(Sure, sometimes 'start-up' is used to describe things like a new laundromat or small consultancy, but the word is more useful when its connotations of novelty and discovery are prominent.)
The Phoenix area has been seeing what strikes me as variants of "start-up porn", with many people and places referring to themselves or their services as in some way related to start-ups. In some cases it's true, but quite a number of these "start ups" are, for example, run-of-the-mill (albeit ambitious) Web design or Web marketing companies.
Now, it's great that people are opting to work for themselves rather than go join some large, likely boring and cumbersome, existing business, but the conflation of "start-up" with "business" makes it hard to really know what's going on here or discuss what people are doing.
Having a reasonably clear and useful definition is valuable.
Seriously, new companies that don't have something substantively different about them don't have good odds. In brick-and-motar that "something different" might just be geographic location (e.g. a car mechanic in a town that doesn't have one), but in the online world, you usually need something more.
The "somethings different" can be only slight changes to the models (better customer service, better support for language X, etc.), but they're always different in some way.
"Startup" can imply something radically different, but it doesn't have to, and in any case, even companies that _try_ to stick to an existing business model rarely do, and the plans always change and adjust as you go along, it doesn't matter what kind of business you're in.
Then perhaps we agree at the margins. It all depends on what you consider to be a 'slight change' in the model. We also probably disagree slightly on what businesses you are willing to claim as startups. Is a new restaurant a startup? How about a consignment store? A dev consulting shop?
Even in the most commoditized industries with extreme competition, there is often a built in profit margin that is essentially accepted by the businesses in that industry, because it would be mutually destructive for it disappear entirely.
I'd wager that most of the small business economic activity in the US comes from sole proprietors repeating business models verbatim and collecting that additional margin above and beyond their built in salary expense.
