Is there a way to update the version of Android?

I have checked for software updates, and system is up to date. From the little knowledge I have a online research it seems many apps want Android version 4.1 or newer and this tablet has 4.0.3 (release5a). Is there a way to get a more up to date version so more apps can be supported? Many apps in the store say they arent supported by version.

Trying to get this old tablet going for my grandma to use, it's been sitting a while but still works! It is a Sony tablet Model SGPT111US/S

Any suggestions?