Engine availability is a major issue
Most designs must pick from a rather small range of suitable engines likely to be available in the design timeframe. Old engines are out--noise, specific fuel consumption, so the menu is shorter than you'd think.
Just imagine that an A380 design person had the bright idea of making it a twin. Other issues aside, the prospect of working over the engine manufacturers to design something so far outside their current range for a modest total units shipped would have stopped this thought promptly.
Though I don't know the history, I'd guess the BAe-146 choice of four engines was likely driven by engine availability, as its short range and other characteristics are firmly in a slot dominated by twins.
You'll notice that long-range aircraft are those more likely to have more engines. With the rule that takeoff must succeed with n-1 engines at the awkward moment implying higher engine count gives less engine weight, the weight benefit of more engines is more helpful at long range (review the Breguet range equation if this point seems obscure).