This question is inspired by the United Airlines Flight 328 where the No. 2 engine is damaged.
Some multi-engine aircraft are design to withstand the detachment of an engine while some are not. Boeing 747 is designed to operate after an engine detaches from the pylon. In 1993, Japan Airlines 46E successfully landed after the No. 2 engine detached from the aircraft (1) In El Al 1862 and China Airlines 358, the detached engine struck another engine. Those are outside of the design scope. On the other hand, the detachment of an engine on a DC-10 would sever hydraulic lines to the control surface as in the case of American Airlines Flight 191.
Many twin engine aircraft are certified with ETOPS so that in the event that one engine failed, the aircraft can return to an alternate airport within the certified time span. However, the ETOPS scenario listed by FAA only includes engine shutdown but not engine separation. (2)
Are there any twin-engine aircraft that are controllable after an engine separation?