Doesn't tell us much without we know the species and grade of the joists as well as the unsupported span, Barry. You may have difficulty with the first two, but you absolutely must know the unsupported span.
Properly gluing the second layer to the first would provide the maximum stiffness, but I would not recommend you do that. Here is
a good article from our Liberry showing what I've come to accept as the very best way to install that second layer.
The quarter-inch plywood must be removed.
My opinion; worth price charged.