Not sure what you mean by bi-directional API? A Cisco router can be setup to connect various systems as a voice gateway, the VoIP protocols that it supports is SIP, H.323, SCCP and MGCP and then it has a big range of TDM (Time Division Multiplex) type connection options as well, such as PRI, BRI, FXO, FXS and E&M. Depending on what the 3rd party system can do you could connect it to your system via a voice gateway.
