The TELCO may have a service like you are describing, but you cannot do it with only a single phone line.

You would need a second phone line with ring-over from the first and then you could set up an answering machine.

With only one phone line you cannot send another call to an answering machine at your office.

Some of the TELCOs offer a service as you describe.
An incoming call to a busy line rolls over to an answering service (computerized) at the TELCO .

You could also do the job with VOIP for the phone service, but that would essentially be creating a PBX on a computer at your house.