"Ah yes, the dreaded seven-engine landing." LOL !
As per the amazing landing on the Hudson river, we actually have an ad on TV that shows that, and interviews the pilot.
He said they ran into a whole flock of birds, so I guess you could have got a bird in any number of engines ?
The very first jet liner, the Comet, had 4 powerful engines mounted in the " armpits " of the wings.
The RAF took over some of the surviving ones to use as air sea rescue, it could fly out to the search area quickly, and then shut down two engines while searching
Back in the 60s one of the apprentices that I worked with at BA ( it was BOAC then ) said that he volunteered as one of the " passengers" on a practice flight that flew up and down parts of England for a couple of hours in 707.
As they were flying around, they were asked over the radio to look out for a missing Cessna, and given the registration number on the wings.
They spotted a small plane on a small grass airfield and overflew it, and all peeled their eyes to see the number, but they were going too fast when it briefly came into view .
So the Pilot went around, and to reduce speed, lowered the landing gear and the flaps to fly over slowly. Evidently the landing headlights automatically come on then.
Everyone peered out of the window, and as they approached the hut, a guy came running out waving his arms in the air and and shaking his head as if to say " you can't land that thing here "