If you have more than one trigger you would still be using one trigger pull to shoot one round of ammunition (double trigger on shotgun is two single shots, not two rounds from a single trigger pull).
Technically I am sure it could be designed and built. Though you would be going into a grey area as far as sears and other registerable parts (NFA) are concerned. Also if you designed a truly single-fire trigger system for each individual shot fired it would become rather large and unwieldly rather quickly. As to be unquestioningly legal it would have to have a separate trigger system and linkage for each trigger. Then hooking up each system to a single firing pin would be rather complicated. Not to mention the economic aspects of building and selling such a system.
In the 1700's and 1800's there were variations of what you want. They were called volley guns. These were generally crew-served by artillarymen. They were basically individual barrels joined to a common reciever with individual firing mechanisms. Similar to a modern modern MLRS (multiple rocket launcher).
As to handheld versions, pick up a copy of Firearms Curiosa by Lewis Winant. Near the end of the book there is a chapter on miscellaneous firearms designs. There are quite a few antique variations -harmonica guns, multi-barrel pistols, Puckle guns among others.