If you have a partial composite beam, and apparently you do, there is absolutely no problem coring and adding steel studs to increase the percent composite action. We have done exactly this on several occasions.
Just core the holes large enough for the stud welder, and at least four times the diameter of the head of the stud for grouting purposes, and be certain that you use a non-shrink grout (at least equal in compressive strength to the concrete slab) to fill the hole. Stud size should be as normally designed for new composite beams.
Also, if you have excessive deflection under the proposed load (or even under the existing loads if the beam was mistakenly underdesigned), jack up the beam slightly before adding the additional studs to transfer the dead load to the composite section.
Strengthening by adding cover plates to the undersdie of the beam is also a relatively simple procedure, which we have done in numerous existing buildings. For economy in field welding, try to use a plate wider than the flange so that the welding is performed in a comfortable position, instead of overhead. Also, design the cover plate and the welding to suit the loading conditions, do not be overly conservative by specifying a continuous weld, and cut-off the ends where approriate. A full length cover plate is never required.
Note that jacking of the girder before welding the cover plate will also transfer the dead loads to the composite section. (Place the plate in position, then jack against the plate, clamping it against the underside of the beam.)