A modem to modem communication system supports call waiting services by exchanging hold request and acknowledge signals before relinquishing the line servicing incoming calls. Thereafter, the modem to modem session is reestablished without having to redial. The hold request may be denied or accepted, and may define the duration a modem will hold before hanging up. The holding modem maintains the session by fooling the higher protocol layers, making them believe that the modem is not on hold. Three-way calling services are also used to free up the shared line for outgoing calls while maintaining the session with holding modems. A table may be employed to screen incoming calls through a comparison of the caller ID information with that in the table. The table may be within the modem or the host computer.