Custom Registration

I am looking for a registration plugin that can allow for custom fields and as selections are made, other registration fields appear. This is for a business intranet registration page. Basically the first questions is what Business they are with (the company has 5) and when someone chooses their answer (chooses the business they are in), the business they chose has its own field where they choose sub business units they would be in.

To take this a step farther, when they choose certain things in registration, they would need to be put into user groups to grant permission across the site. So that when they choose their selections in registration they are automatically put into the right groups.

Does this make sense?