You could use a pair of large clamps close to and flanking the screwhole to prevent the screws from pushing the plies apart. Once the screw is in at full depth the clamp is removed. It might take four clamps--from both edges of the beam.
Also you might want to use wax or other appropriate lubricant on the screws and be careful to avoid making the "pilot" holes too small.
If the pilot holes are properly sized (large enough), then there may be no significant separating force and so clamps may not be necessary. If you don't have clamps, try it without them and see what happens. If separation occurs you can always take the screw out and get some clamps.