Are there some kind of boxes to plug on an RJ11 with two outgoing RJ11
> plugs, that can tell if an incoming call is voice or fax, and direct
> the call to the ad hoc plug, either a handset or a fax-modem?
Some FAX machines have this builtin, for instance some Panasonic models. Daisy chain from line to FAX to answering machine. The FAX lets the answering machine start every time, but the FAX intercepts (and hangs up on the answering machine) when it recognizes the FAX tone. If the FAX has a handset then you can answer manually, then push the START button on the FAX as necessary. On an ADSL line, remember to insert the filter before the first non-ADSL device.