alt Hacker NewsEven for a standard PC, you could buy a 16 port serial card and hook it up to 16 modems, either discreet devices or the dedicated ISP kit which might support dozens of incoming calls (possibly on a single bearer) via various means. Telebit netblazers and then ascend maxs were common in those days.
The question is if you could actually handle that many lines concurrently, with available software and the hardware resources of a single PC. Rachel's article as well as other comments here indicate that you could not.