It may seem best to start with a perfect secure network design from the ground up. Take into account all aspects of security and process and the end result could be amazing. Building something from scratch often seems easier than fixing an existing system or process. But if we are limited by our unique circumstances not building new doesn't mean we should just stay where we are.
Sometimes we can start fresh and create something; learning from our history and tapping into our knowledge garnered over the years. Othertimes, you have to renovate. Both ways have the ability to produce an amazing end result. Secure design can be achieved in any scenario. You just have to start the process.