Mine's not wired and has batteries in button and receiver unit. Believe you can buy these with more than one receiver. Otherwise with what you want, you can try searching for some sort of wireless attachment for what you have.
Maybe use a "Baby Monitor" setup. Sending unit near the bell/chime. Receiving unit on the patio. Also becomes portable if needed in garage or basement ?
wire a relay into the existing circuit to close the contacts on a "wireless" doorbell button - take the "chime" onto the patio. Just a little reed relay will do the job because there is virtually no current required.
*I installed the Extend-a-Chime for a customer. It has a little device that gets wired into the door chime and a remote plug-in module that chimes when the doorbell button is pushed. I think that Smarthome.com has them.
I did just that. I started with a cheap wireless doorbell, but I certainly didn't want two buttons at the front door, and I didn't want to have to maintain a battery in the button.
So I took the button contacts in the wireless button and ran a jumper between them so they were always closed, and I ran wires from the existing transformer to the the battery connector in the new button.
Well, one wire started with the wire that was only hot when the existing button was pressed. Then I put in a small diode to change part of the transformer output to DC. My button was iirc 9VDC and I have the higher voltage transformer, which I think is 18 volts, or lower. So rectified it came out to 9, the rectified it came out to about 8 or 9. The wireless button is attached to a floor joist, next to the transformer and basement door bell.
The receiver is plugged into the 2nd floor hall.
If someone is really quick with the button, they can ring the front hall and basement bells, without giving the button enough time to start the second floor noise-maker going. But so far, I don't think that has happened for others, only for me during testing.
I see a potential problem.... What if you are next door sponging tools off the neighbor.... You might consider replacing the interior sounding unit with something like this....
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