Good about the applied dynamics of growing companies (including software companies)?

Question

Startups

Interested in materials and books that describe the experience of managing the growth of companies. What happens when companies grow through 5 people, 20 people, 50, 100, 1000 people in the state. I will leave out the success of the enterprise itself in this question - a priori we believe that the business is successful, but now the team needs to keep up with the market. How to ensure such growth, what to take into account, what should not be done, what are the general patterns.
There are particular examples of such materials, such as Ashmanov's "Life inside the Bubble", but this is not enough - the mythology and the original presentation in the form of a story in such books overwrite the practical essence. And here are some general patterns in question: it is known that for successful growth it is necessary to ensure that the company has a minimum composition of leaders. If you do not have 4-5 leaders (growth points, self-driven people) for 20 people in your current staff, then the company will not grow. Further, we are interested in going deeper into this issue - who conducted what research, etc. It strongly resonates with social dynamics - like those very 5-10% of influential vertices in social graphs that determine the behavior of the majority (and they, in turn, are very well studied).
Often the issue of growth is solved by attracting third-party leaders with experience, who then (often successfully) replicate it. This is coupled with the replacement of the team, leaders often collect their proven team from previous places. But it is naive to believe that the matter is only in the team itself. Obviously, this team has the same experience of growing or, if you like, growing. Interested in a description of such experience, preferably in application, including to software companies. We are not interested in particulars, but in general patterns, i.e. which is typical not only for Apple or Microsoft.

Answer 1

That is, you look at the company's success through the prism of the ratio of the number of employees and leaders?
It is probably better to look at the level of problem solving and human resources through adequate capabilities that can be "touched" rather than ephemeral and unusable models.
Or I misunderstood something...

Answer 2

I tend to believe that there are no universal abstract paths. If we talk about software companies, the growth paths in outsourcing companies and product companies are already very different, including the "type" of key people.
In your model, growth = more jobs, which is not entirely true in the IT world. For example, the creator of Minecraft experienced the growth of a company almost single-handedly, and the world is full of companies with up to 10 people whose turnover could be suitable for companies with a hundred employees.