Install another Settings app? Is it possible to install a different settings app than the one my phone came with?  Specifically, I'd like the official Google one.
There's an alternative method here if what you're looking for is greater control and access to settings not available through the default settings UI: Settings Database Editor

Word of warning: you can possibly brick your phone if you don't know what you're doing, so proceed with caution, back up your data, and thoroughly research any customization.

Through this app, you can directly access and modify the db values for your various device settings.  This doesn't necessarily require root (might depend on device model &amp; OS version), as you can grant some of the permissions through an ADB command.

EDIT: fixed link.