Private-branch exchange that provides call bridging to an off-premises terminal in the presence of a third-party application

A method comprising:

• transmitting from an application server, a notification that an active call exists between a telephone number D and a telephone number T, wherein the notification is transmitted to a telephone number C;
• receiving, at the application server, a request to bridge the active call to the telephone number C, wherein the request is transmitted from the telephone number C;
• and
• in response to receiving the request, bridging the active call by:
• (i) allocating, from a pool of ports at a private-branch exchange, a port P that is capable of emulating a telephone extension, wherein the extension is known only to the application server and to the private branch exchange;
• and
• (ii) establishing a resultant call between the telephone number T and the telephone number C, the resultant call being based on the active call and on at least one precursor call having been made that includes port P, wherein establishing the resultant call comprises:
• (1) enabling a capability that extends calls to the telephone number C that are placed to the telephone number D;
• (2) directing a first precursor call to be established from the port P to the telephone number D;
• (3) directing the active call to be placed on hold;
• and
• (4) directing a second precursor call to be established from the telephone number D to the port P;
• wherein the telephone number C is associated with the telephone number D in a data structure and is within the address space of the Public Switched Telephone Network;
• wherein the telephone number D is within the address space of a private-branch exchange;
• and
• wherein there are already established connections between the telephone number T and the private-branch exchange, and between the private-branch exchange and the telephone number D.