You can add a new case. You can change up your ringtone. You can set the picture on the lockscreen. You can even root or jailbreak your phone for more internal customization. But it ain't really going to change what you have there: a mass-produced piece of electronics.
Now, with the RePhone DIY Cell Phone Kit, you can build your phone from the ground up. It's an open source modular phone kit that you can use to provide the ultimate customized device or use to convert your plain old boring toilet (or whatever) into an Internet-Of-Things toilet. *cue angelic music*
The kit comes with almost all the parts you need to get going, including a RePhone Core Module GSM + BLE, an audio module, a 1.54'' touchscreen, a 520 mAh battery, and two precut kraft paper "cases" for you to create a phone in minutes. You'll need your own 2G Nano SIM card. But once you have one, you'll have your creation making and receiving calls, sending message, and playing music before you know it.