Submissions question

I am creating forms for various baseball leagues and events on my website. I’m thinking I’ll need to limit the number of people that can register for the various events when the site goes live.

Example: The link I gave is to one of the pages, Fall Ball (Boys)…so parent’s will be able to register their kids to play in the Fall Ball league. I’m guessing (although the person that is having me make this site hasn’t confirmed it) that there’s going to be a certain amount of people that can register, and it’s closed off after that amount is reached. Can I do that through Contact Form 7 or with any of it’s plugins?

The page I need help with: [log in to see the link]