By applying multivariate testing to their phone tree using Twilio, a company can gain insights into various aspects of their IVR system, such as the clarity of options, caller completion rates, and user experience. They can scientifically test hypotheses about their menu structures and content, making data-driven decisions to improve customer service. The process involves creating a new Content class to separate structure from content, modifying the Step class to use this new approach, and updating the call_handler.rb script to accommodate variant selection and metric updates. With these changes, the company can iterate on their IVR system, applying continuous improvement and optimization techniques to enhance the overall customer experience.