You can ask your phone company if they have call waiting and if so how much it would cost you to have it added to your phone package.

But with a dial-up ISP connection I am not sure how that would work. Your dial-up modem, (whether yours is inbuilt into the computer or an external modem), might lose the connection if you have this added to your phone line subscription.

But I got this from a UK site;
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"Dial up connection failures can also happen when you receive a call while you are accessing internet through your phone line. At this time the modem may drop the connection. You may avoid this issue by having a modem with call waiting feature. The call waiting feature allows a modem to stay connected to internet while an external call is received. At the same time the modem signals the user that a call has been received.

The call waiting feature can be kept enabled or disabled per your requirements. If call waiting is enabled while you are using your dial up connection then the modem connection will be interrupted when the cal is received. On other hand, if the call waiting feature is disabled then the modem will notify the user about the received call but the connection will not be terminated immediately. When you sign off and your modem hangs up the phone, Call Waiting is reactivated."
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So it seems you may have to look into a specific modem that has the call-waiting feature. The site I got that from is;
http://www.free-dialup.net/free-dialup-uk-articles/best-dialup-uk.html but as it is UK I am not sure how much it will help.

Mark