Overall, the team structure is mentors, over the team captain, over the student leaders. We have three departments, which is purely organizational and does not have a leader over them. Inside of the departments are our subteams which DO have leaders. We have departments because the students and leaders often help with the other subteams inside that dept's tasks (ex. HR lead will help Finance contact sponsors). We refer to student leaders + mentors as our "executive board" or team. Here is an easy easy way to understand our structure -
a fancy image!
Engineering Design - Mechanical, Electrical, Programming, Game Strategy
These are all self-explanatory.
Branding Design - Communications, Products
Communications does website, social media, helps with awards. Products designs shirts, banners, costumes, pit, etc.
Business Relations - Finance, Human Resources
Finance raises and does some managing of funds (mostly mentors for latter). HR helps build relations in the team by making sure everyone has something to do, and also helps build relations with other teams.
As you can see, there are four engineering leaders and four non-engineering, and the Team Captain makes the final odd vote. This is a good, healthy balance for the team in making decisions.
To answer the rest of OP's specific questions: we've discussed it many times as a team, and we stick to having one team captain for a variety of reasons. One is that there needs to be total accountability and we can't have the captains contradicting each other or any type of confusion on that front. Another is the balance I discussed before, and frankly, it is already sometimes hard to find people to fill all leadership positions anyways and adding another wouldn't help.
Our team has about 40-45 students.
There are a lot of teams in here with "dynamic," changing structures and a crazy amount of leadership roles. Our team made a specific decision two years ago to set our roles concretely, and every leadership position has a specific role and contributes to a healthy team balance. We also think it gives students a goal to work towards - students can show initiative in specific teams to show they want to earn that leadership position (which is elected by the earlier student leaders). Even though this structure was developed sort of closed-door with two students and a mentor and enforced immediately, our team has really grown to it and really believes in it. At our Business Summit we hold for teams, one of the biggest things we emphasize is that having a strong organization structure can make for a strong team.
Happy to answer any questions about our structure.