New calls destroying current ones?!

We’ve dealt (or are dealing) with the typical dropped calls, but one customer noticed that it seems like new calls make current ones drop. I didn’t believe this until people in this office were moved into closer proximity and could hear each other making/breaking calls.

Now, I know Asterisk can do this with some fancy, emergency 911 logic, i.e. blow away a channel/trunk that’s inuse if there’s no available line for 911 outbound, but is there a dialplan (mis)configuration that could do the same thing? As in, the box doesn’t have enough SIP lines but instead of ringing busy it sets up a new channel regardless …