Maybe someone who is more of an expert can "chime in" (sorry, couldn't resist the pun), but I don't think there is a way to do this, as you can't add a second Touch Screen.
Comcast offers a siren repeater so you can hear an alarm going off if you have a large house and need another siren, but I don't believe that would sound the door chimes.
There may be a creative way to accomplish what you want to do though ... there are devices called "Power Failure Alarms" you can buy that alert you to power outages (useful if you have a freezer in the basement, for example, and a breaker trips causing it to lose power).
In this case though, you could connect one to an XFINITY Home Lighting Controller (which would normally be used for a lamp or other appliance).
Once you have the Lighting Controller connected to the XFINITY Home system, you would keep it turned "On" all the time. You could then set an XFINITY Home Automation rule to turn the Lighting Controller off for say, a minute, every time a door opens and/or closes. This would result in the Power Failure Alarm to trip and sound an alert.
I found one online that's not too loud, and includes a light too. http://www.amazon.com/Reliance-Controls-THP207-Failure-Flashlight/dp/B000IF8QDK?ie=UTF8&keywords=Power%20Alarm&qid=1465411714&ref_=sr_1_15&s=hi&sr=1-15
You could also accomplish the same thing with just a lamp connected to the Lighting Controller if you don't need an audible tone. The lamp would turn on for a minute every time the door opened and or closed...
Private message me if you need more details or help finding equipment. I love coming up with creative ways to use XFINITY Home. 