Upgrade from 4.3 with root

So currently my note 3 is running android 4.3, has root, and I believe has an unlocked boot-loader. Otherwise stock Rom and Recovery.

My question is what can or can't I do to update my phone to a newer version of android while maintaining root.

On a side note anyone know if newer android versions improve BLE support? It's practically non-existent on 4.3

Thanks in advance.