A BAe 146 operated by an NFD crew got airborne at night from Genoa. They went straight through a flock of seagulls which took out 2 engines immediately. The crew did a fantastic job - quickly round the harbour in the dark at 500 feet - which was just as well for the 3rd engine failed on finals!
On both occasions the crew were very practical and not too concerned with the theoretical!
Multiple failures from birdstrikes are not as uncommon as you would seem to suggest. I just hope that you never have to deal with such a scenario.
They are only as common as those truly verified in data bases. I also don't recall a BAE146 being in the data base.
The data base has a singlular use to promote changes to improve safety. What's not verified in the data base will not be addressed.