"To escalate the issue" means to make the problem or situation more serious or severe, usually by involving higher authorities or using stronger measures to address it. Full definition
Responsibilities include updating event details across multiple platforms, confirming scheduling changes, reporting sales information, menu inventory management, and escalating issues as necessary. (flexjobs.com)
The idea of starting at the branch level is to have reasonable people ask reasonable questions and see if you can all come up with a reasonable solution before escalating the issue further. (moneysense.ca)
Sometimes it can be challenging for a couple to be kind or thoughtful of each others needs or find the time to talk about current problems without escalating the issues. (psychologytoday.com)