I've never understood why a startup would choose to grow to the size where it needed two layers of management, unless the individual product they were working on was really of a complexity too high for a small team to manage (like, say, a nuclear reactor.) For products that stay the same size, but gain new sub-products, cross-products, side-businesses, etc., why not just "undergo mitosis" and become two startup-sized companies, each handling a single facet of the business but sharing a treasury and building?
There was a company (BSO) that did just that, they split every time they got to a certain number of employees (I believe the magic number was 50). They were hugely successful.