I would not rely on any form of "adhesion" of new to the old.
Kinda depends on why the increase in size is necessary. Consider that the existing concrete has probably undergone most of its shrinkage. The new concrete will shrink with respect to the existing, and will compromise the bond that you're looking for.
If you need the additional cross-sectional size for compressive forces, then your encasement method may work. I would roughen the existing surface, use a good bonding agent, and provide shrinkage/temperature reinforcement using more frequent small bars rather than large.
If you need the additional cross-sectional size for tensile forces, I would consider casting an additional beam (or 2) next to the eisting with no attempt to bond to the existing, then concentrate on developing the end anchorage into the footing or cap at each end. Any shrinkage cracks that develop will be distributed over the length of the new beam(s) and should not be of a size for concern.
Ralph
Structures Consulting
Northeast USA