I think most jurisdictions have implemented an official appeals process that adjudicates issues by a specially selected board. Usually the board members are made up of both AHJs and Industry members so that a balanced and common sense decision can be made regarding the appeal. The problem most times with this process is that the appeals board only meets very infrequently and waiting around for the scheduled meeting doesn't really offer an expeditious solution for a project that is working under time and budget constraints. The reality is that there are often times other means and methods to solving a code based denial of your permit.
Many times it possible to hire a professional, like an engineer or specialist to help you draft an Alternate Means and Methods Request for the specific issues. Basically, you can try and find a more desirable way to achieve the end result that the code is designed to achieve. Most people think of the code books and regulations as black and white, but they can be very grey in certain areas. As long as you end up with the same end goal, then you can explore many different way to get there by consulting a professional who can offer you more creative ways to achieve your end goal in the most expeditious and cost effective manner that meets your project goals. This can be expensive because some professionals charge a high fee to do this kind of work, but sometimes it's worth it to pay. And the fact of the matter is that once the AHJ has a licensed, experienced, and trained subject matter expert to produce a document that says the desired request is compliant, safe and meets the intent of the code, they are more willing to approve your request because they have liability protection to fall back on if something goes wrong.
Another method is trying to push the issue up the chain of command. Every person who makes a decision regarding has a boss and that boss has their boss as well. And when you follow the chain all the way up, you usually end up at "we the people" who elect the political leaders of jurisdictions that are ultimately responsible for adopting codes, ordinances, and regulations that the community has to follow. While it doesn't always result in successful outcomes, reaching out to your elected officials could help resolve an issue, especially if it's one that is based in common sense that the general public would support or if it's a policy or procedure that is bad for business overall. If you can gather support of the community and put pressure on those politicians then you might be able to push the scales in your favor through political pressure on department heads and directors. This can be an arduous process but sometimes is the last best option for avoiding the undesirable situation.
I hope this is helpful for anyone who is trying to look for different answers than the standard, NO.