If you are looking to expand your horizon, since you said that you are desktop support, can I assume that it is in a Windows environment?

What about looking at MacOS deployments, dealing with MDM and device management software such as JAMF

In the field of security, then it would be Endpoint security, setup, deployment, project manage for desktop support

Then towards managing remote support, managing a team of support engineers to support your users remotely vs onsite (depending on the more cost efficient route).

Then work your way towards owning the entire desktop/laptop experience for the company.

That is usually the path I see for folks within your area of purview.