I have a number of phones which all display caller
> ID as well as a voice modem on each line for answering machine
> functionality.
I believe that, as with ringers, there is a limit to the number of caller ID devices you can put on the line and still have them work. It is quite possible that, for the purposes of this question, modems count as caller ID devices.
No, I don't know what that number is. Likely it depends on the particular hardware, as with ringers, and the particular telco equipment and wiring.
I'm sure someone else here will be able to provide a more authoritative answer.
Dave