If I had to structure an organization of 1,000 people, here's how I'd do it: rather than tiers of management on the order of 1, 10, 100, and 1000, I'd just have two levels. At the top would be a small committee that controls allocation of money and from time to time publishes non-specific guidelines about where they'd like the company to go. One person on the committee is in charge of hiring salesmen, who once hired are basically unsupervised and work for commission. The rest of the company is a bunch of small engineering teams of up to 10. All functions other than sales and engineering are outsourced. The most senior member of each team has hiring/firing authority for that team. He gets to decide the size but 10 is the max. These generate their own ideas and speak to the controlling committee only for budget requests. Salary is not part of the budget request: everybody in the company gets the same salary. Bonuses are awarded to teams that implement profitable ideas. More money goes to bonuses than to salary. If a team shows a pattern of underperformance, the committee fires the entire team. If this happens, they get 30 days notice that they're going to be fired, and they can use that time to find jobs on other teams within the company.
If I then had to scale this to 10,000, I still wouldn't add another layer of management. Instead I'd just add more teams, and expand the controlling committee to a confederation of committees, which all draw money from the same pool but have specialized expertise. When teams request budget, they approach the committee with the best understanding of their proposal.
The 1,000 person model looks a lot like a bunch of founding teams and one VC firm. The 10,000 person model bears some resemblance to the federal government, which is perhaps why an organization the size of the government manages to function at all, however poorly.