Handrail in center of stairs?
The Code requires the stair width to be 36” ABOVE the handrail and 27” width at the handrails and lower. (See IRC R311.7.1)

Only one handrail is required. (See IRC R311.7.8) (In commercial projects, a center handrail is required every 88” width of stair, except at historic structures.) Also, handrails are required when you have 4 or more RISERS. (See IRC R311.7.8)

Handrails can project 4 1/2” and should be between 30” and 38” above the nosing of the tread. (See IRC R311.7.8.1)

BTW, in olden days, the handrail was required on the right side descending. This is no longer required. 

I agree with @JimStewart and I’d install a handrail on the sides and leave the center open to allow you to have that new barbecue easily delivered up on that upper deck.