If your current job isn't all it's cracked up to be, why not think about expanding your existing job? While job descriptions can sometimes feel like a strait jacket, they don't need to be and provided you're bold and confident, with some strategic thinking you can turn your job into something a bit more exciting, dynamic, and suited to your evolving skill set. Move boldly where others have forgotten to tread...
Look for unfulfilled gaps. These are the gaps through which unsolved problems fall and there are always some around. If you can see solutions and nobody else is paying them much attention, they are there for the taking. Spend a little of your time taking these under your wing and work away at them. In many cases there won't be a need to ask for permission; it will be a case of an evolving interest and can serve you really well to advance if you find ideal solutions. For more advice on finding problems to solve, see How to Define a Problem.
Note the opportunities as they arise. If you have a gift for noticing how things could be done better, more clearly, faster, etc., note them down and work through them when you can. Learn How to Be Proactive. The more little solutions you can tuck under your belt, the more your initiative will be noticed and applauded.
Make sure that working on these issues is not detracting from your properly assigned job and make sure the gap problems are worth solving. It will harm your career or trade trajectory if you're not doing your job properly, so make sure that is taken care of before taking on additional tasks. You might even need to devote some personal time to the gap problems but if you consider that solving them is worth it, that will be of benefit to you. To help you work out whether it is worth attacking the gaps, ask yourself:
Think about who else you might bring on board to either help you expand your job or support you generally. If other people can confirm that what you're doing is needed, essential, and useful, then you're more likely to get managerial buy-in.
Find ways to present your solutions clearly. Be organized about your solutions and keep records, notes, photos, etc., of progress and results so that you can demonstrate the improvements with ease. It also helps if you can develop something of broader utility, such as a manual, a system, or even signage that helps colleagues to benefit as well. Be prepared with fast, pointed, and accurate explanations of how your solutions have improved the workplace.