Something I haven't heard of for years could be involved. In the UK at least there was a limit to how many extensions you could run off a phone line. A line had a limit of 4 REN ("Ring Equivalent Number", whatever that is) and each extension was normally 1 REN though specialist units might be higher. Some early modems were REN 3, meaning you could only run one extension plus that modem on a line. Once you exceeded the limit the phones didn't necessarily stop working, but you could get various odd effects.

As I say, I haven't heard of this being an issue for maybe 10 years but you never know.