I agree that all 4 engines can be knocked out by something like volcanic ash. However I reiterate that no 4 engine jet airliner to my knowledge has been lost by continuing after an engine failure and having a further loss of engine power.
Kalitta B742 at Bogota on Jul 7th 2008
Crash: Kalitta B742 at Bogota on Jul 7th 2008, engine fire, impacted a farm house
- a non-recoverable surge of engine #4 during rotation resulting in the loss of engine power, the combined effects of an inefficient high pressure turbine, excessive slack space at the tips of the blades, reduced chord and leading edges of the fan blades and the high altitude contributed to the engine failure.
- an undetermined anomaly in engine #1 which manifested itsself in engine surges and resulted in the loss of engine power. The failure to maintain proper minimum aircraft speed during climb out and the resulting use of emergency extra power exposed the anomaly leading to the engine failure.
Granted, this was not a case of a 4 banger attempting to continue to destination after loosing an engine at TO, but it did crash due to the independent failure of two engines.
I can think of a number of incidents and accidents due to multiple engine failures due to 'common cause' - usually environmental such as adverse weather, volcanic ash, and birds. While I suppose one could make a reasonable argument that more than 2 engines is an advantage with birds (less likely to get critical bird strikes on all engines), for extreme weather or volcanic ash the number of engines makes little difference. Just off the top of my head I know of at least two 747 four engine power loss events due to ash, and two 747 three engine power loss events due to extreme weather (fortunately all ended happily).
I can't think of a single twin accident due to independent power loss on both engines, yet it took me literally seconds so come up with a 4 engine accident due to independent power loss on two engines (it helped that I was involved in the investigation
)