> Also, what's a typical path going from a team manager (EM1) to senior manager (EM2)? What are the things I should focus on to show I'm ready for managing managers? (I understand it can take a few years)

(Qualifications: Director-level with several managers reporting to me in 60 eng org.)

You got a lot of answers for the first part, but not much for the second part. For the second part, I would recommend reading "The Manager's Path" by Camille Fournier. It's a great, short read that really lays out the different roles and responsibilities at different levels, and it does so at a high enough level that it should be relevant to most companies.

More concretely, this is a conversation you should have with your boss! The criteria for moving up in your career can differ from company to company, and your boss is going to be your best ally to get there. (If your boss is NOT interested in helping you, find a new boss!)

That said, don't skip too far ahead. Focus on doing a really good job with your own team, and once you've got that down and rock solid, then start to think about next steps of taking on multiple teams. It's kind of a totally different beast to manage multiple teams, but having the fundamentals down will make it more incremental than it would otherwise be. It's good to have a milestone down the road, but put 90% of your effort toward the short term and 10% toward making sure you're still moving toward those goals.

Good luck!