It is FIOS POTS. There are 2 NID's bringing in the 5 lines and both were changed by Verizon.
There appears to be no echo when pressing keys heard either, from your cell phone, butt set or land line. It only happens intermittently too, roughly a few times per week.
I have heard a tone after dialing the second digit, just as I press the 3rd digit for the extension, sounding like an error beep, meaning it has already received 3 digits and cannot allow a 4th. That's when you get sent to the incorrect extension. Example 113 instead of 137.
