My advice would be to do what my own team is trying to do right now (we doubled our team size this year and only have one additional mentor).
Parallelize, parallelize, parallelize. We are currently working to ensure we have a flatter leadership structure wherein different mentors, and different key students, fully own different portions of the team. Trying to have a couple people at the top getting involved in every aspect of the team can quickly become impossible as a team scales.
The real question though, is how to execute this. I'll explain what we are doing in two parts:
Students- We are holding required "leadership seminars" for students who will be holding leadership positions on the team. At these we are focusing on accountability as a leader and how to actually be a leader (from "How to win friends and influence people"). Letting students fully own projects / aspects of projects will be needed for our larger team.
- We created an "Elders Council" made up of mentors and select students to make "strategic decisions requiring expediency". That covers decisions where we think students should have input, but don't want to slough through a conversation with the whole team.
Mentors- We no longer have an overriding lesson plan that addresses each sub-team. The different aspects have been handed off fully to mentors leading those groups, meaning that those mentors plan every aspect of their sub-team's training. Sometimes they are even holding additional meetings for individual sub-teams.
- We have a week to week lesson plan that covers general activities that are useful for a FIRST team. Teamwork / leadership activities that revolve around building or some other aspect of FIRST, build challenges that require mechanical, electrical, and programming aspects, etc.
- We are having more frequent mentor meetings (~15 min following a meeting) to discuss any goings-on with the team that we may have missed.
- We also started a parent booster club in order to take some of the load off of mentors. We had to have one of our mentors as the president of the booster club though, as none of our parents wanted to step up.