Nope, it cannot go beyond 10.13.6. The reason being is Mojave requires a GPU that has Metal, that functionality was not available until the 2012 iMacs were introduced. And before you ask, no your iMac cannot be upgraded to have Metal GPUs. If you want to go beyond 10.13.6, it is time to buy a new Mac. You may want to consider one of the new Mac minis, extremely fast and Big Sur was optimized for the M1 processor.
Note: If you run any third party 32 bit apps, they will not run. This means they must be updated or replaced before running Catalina or later versions of Mac OS.