What software can I update to for a Mid 2011 iMac

A 2011 iMac cannot update to Mojave. It's simply not possible.

Note the requirements for Mojave here: How to upgrade to macOS Mojave - Apple Support

10.13 High Sierra is as far as it goes.

As mentioned Mojave requires a Metal capable GPU which is not available in iMacs made before 2012.

To update to High Sierra see here: How to upgrade to macOS High Sierra - Apple Support

The last update a 2011 iMac can do is 10.13.6, Mojave requires the GPU has Metal. Metal was not available on iMac GPUs until 2012. No, your 2011 may not be retrofitted with a GPU with Metal.