If it is a 2011 or earlier iMac 10.13.6 is the maximum it will go to. If you need later version(s) of Mac OS then it's time to buy a new Mac, sorry but it is that simple. Mac OS (Mojave and beyond) rely on GPUs that have Metal, this became available in 2012 iMacs. Before you ask, no you cannot upgrade to get a GPU that supports Metal.
If you do decide to buy a new Mac (wise decision) you may have old legacy apps that are 32 bit, these will not run on Catalina (1015.x) and beyond as they require 64bit apps. You can download Roaring Apps and that will help you determine what apps you have that are 32 bit. If you want those apps to run in Catalina and beyond, then you will need to upgrade or replace those apps. Technology moves forward and Apple has warned us for years they were moving away from 32 bit applications.