dial-up server catch-22

[Gregory Nowak]

Hi all.

I have been seriously considering the idea of setting up a dial-up server for myself, in the event that I want to access my machine,
but have no access to a network, only to a phone line.

My problem is though that I have an answering machine, and only 1 phone line.

Is there some way to setup init/agetty so that the modem would answer the phone on every other call?

A scenario of what I mean by that is as follows.

1. I call in, and remotely disable my answering machine.

2. I call in with a modem this time, and say my server is set to pick up on the 6th ring, which it does.
I then login, do whatever I got to do, and end the connection.

3. I call in again, but the modem knows this is another call, and doesn't pick up.
This would give my machine a chance to pick up after 10 rings, so that I can reenable it.

Then, in the future, if I disabled the machine, and let the phone ring 6 times, the modem would pick up.

Then, if I called in once more, it wouldn't pick up, and so on.

Could someone please tell me if what I'm suggesting is possible, and how 
I can accomplish it?

Thanks in advance.

Greg