Not with a A800. The caller id is “inserted” on the central office, when the call goes trought.
If the phone company will not offer a service to turn it off, there is no way to disable the caller id.
The best thing to do will be asking for a “hunt group”, with the same phone number on all the lines. Some companies will do that.
Then order a extra phone line, and put a answering machine on it with a recording that says “this number is not in service”
If anyone gets the caller i.d. from the calls ands try to call back, they will hit the first line with the recorder, and go away most of the times.