Google has chosen to keep the on-screen navigation bar simple ever since it was introduced back in Honeycomb. It's changed a little bit over the years, but Xtended NavBar lets you change the way it works without screwing up the UI. When you need you navigation buttons, they're in the usual spot, but you can swipe to access more functions.
If you've ever used the multiple home screen docks in an app like Nova Launcher, this is a similar idea, but with the nav bar. The "center" view is your standard nav buttons, but swipe one way and you get playback controls. Swipe to the other side and that's a quick settings bar. You can arrange these however you like, and there's also a favorite apps list that you can get by upgrading to pro via a $1.99 in-app purchase.
This app requires the Xposed framework (it's a module), so it's for rooted users only. Additionally, you need to have an on-screen nav bar in the first place, and it works best on AOSP-based ROMs – no promises beyond that. Proceed, but do so with the correct amount of caution.