Adjusting the threshold for voice mail to answer to be less than the rings before the call goes to the next line or phone company voice mail is one solution.
Most of the time it would be appropriate for the customer to call their service provider to "roll on busy" but not "roll on no answer" or extend the number of rings before calls roll to subsequent lines or before calls roll to voice mail.
Example. AA picks up at 4 rings but lines roll on 3 rings. Line provider would be required to extend to 5 or more or stop rolling on no answer.
Lec applied their voice mail to answer immediately