The door is probably an SLT extn that is programmed as a hot line when the button is pressed, have a look at the endpoints or phones section in programming. You'll probably see one marked as door.
You need to determine whether this extn rings a group or straight to a phone, if its a group add the phone you wish to ring into the extn list.
If it currently rings straight to a phone you'll need to create Hunt Group Extn list, add the phones you want to ring into it, create a hunt group then enter the HG extn list into it as a member.