Telephone line shared by two modems

I need to share 1 line between Fax software (Zetafax) and Internet access on Windows NT. The modem is on the server. The problem is that Zetafax owns the serial port and it does not allow the proxy (Wingate) to get access to the modem. It can be solved if you shutdown the Zetafax server or service when you want to connect to internet and bring it up again when you finish with internet but that is no suitable because it would bother people too much. My idea is to put 2 modems in 2 ports sharing the phone line, and I wonder if there would be any problem when one software is using one of the modems causing something to the other modem. Another solution would be to use the command option of the dial up definition to shutdown the fax server when you want to use internet but the problem would be to bring it up automatically. I need a good solution for this problem.
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If one modem is using the telephone-line,
then activating the other modem will cause the detection of a "busy" condition (i.e., lack of dial-tone).

It shouldn't cause enough interference
to cause the "active" modem to "drop" the current connection.
From the way I read the question then yes by adding the second modem you can access the internet with one while the other is still waiting for incoming fax (although it will receive none)
The Fax software holds the modem as long as the software is running, that does not mean it ties up the telephone line, it holds the modem waiting for incoming fax (or outgoing) but it does not take "phone off hook" so with the second modem you can access the net without disabling the fax software.

This is along the same line as you are able to make a phone call on an extention while the fax software is running, (as long as it is not sending or receiving)  While the sofeware is waiting (to send or receive) the phone is "on hook"

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