I've had such systems running at 9600 bps, but they often drop connections and are quite frustrating. Don't push your luck.
One solution is to have a computer at the landline location connect to the Internet and share the connection over the LAN. If it's not on all the time, put it in sleep when idle, then use wake-on-LAN to bring it to life from a remote PC. Or, get a router/modem that does all that automatically.
Another possibility: If your LAN is wired Ethernet, using Cat-5 or better, but is not Gigabit, then only two of the four cable pairs are being used. Steal one of the remaining pairs and extend the landline to the remote site that needs the modem.
