Would it be beneficial for the Boeing 777x to have a biplane wing design?
A major disadvantage to that design would be the aft wing had a disrupted airflow over it as it travels through the fwd wing's wake, so lift is greatly diminished.

As to doing a stacked biplane design typical of small sport biplanes in use over the years, this is probably frowned upon for two reasons:


High Drag - more structure in the relative wind always means more drag anemic this was one of the major advantages to the cantilevered wing developed in the 1930s.
Heavier - more wings means more structure both in terms of the second wing itself plus the mounting structure to mate the wing to the fuselage.


A single cantilevered monoplane is by far the most efficient solution save only a flying wing, but these are not commonly used in commercial travel which has been discussed in previous threads.

Now that's not to say a biplane may not be useful for commercial aircraft.  Researchers at MIT proposed a supersonic biplane design which usea the configuration to dramatically reduce its sonic boom.  



Whether this idea survives the CGI proposal and becomes actual hardware is another story; this business is full of concept aircraft and precious little flyable hardware.