Your question does not distinguish between administrative privileges, and "highest privileges possible".
Where to go when you have elevated privileges?
"Elevated privileges" are not the highest you can go. Even though you might be administrator, the operating system kernel can still deny you access to some resources or to perform some actions. Furthermore, reinstalling the operating system will wipe your access (as long as the new system is not vulnerable again).
So in short, when you have elevated privileges, you can still get kernel privileges.
Where to go when you have kernel privileges?
When you have kernel privileges, you act as the operating system. Nobody can deny you access to resources, unless they were designed not to be accessible by anyone, because there is nobody to deny you.
This might seem like the ultimate privilege escalation, but you can still go further and become the Hypervisor.
Where to go when you have hypervisor privileges?
Have a look at this chart:
On a system set up with a Type-1 Hypervisor, several operating systems can run in parallel. Even the kernel of one operating system has no access to, or is aware of, the other operating system.
However, an exploit in the hypervisor could allow you to take over the hypervisor and give you complete access to all operating systems on the machine.
So where would you go from here? If you imagine the operating system bubbles in the chart to contain a "user space" and a "kernel space", then we gradually moved down from the privileges of a normal user, to the privileges of an elevated user, to those of the kernel and now to those of the hypervisor. It would only make sense to keep moving down, which would lead to the firmware, the abstraction layer between hardware and software.
Taking over the firmware would allow you to persist your malware, even when the operating system or the hypervisor are wiped clean. The only way to go even further is to exploit the hardware directly, as is the case with some hardware bugs.