But the PNF who pressed TOGA is expecting it and can help an overloaded PF by taking control or applying pressure or trim.
I would have thought the last thing you want is having both pilots putting inputs into the controls at the same time and possibly in opposition. Recipe for confusion and disaster.
If the PNF is actuating the stab trim without the PF being aware of it, it is possible the PF may think he has a runaway (uncommanded) stab trim movement and act as per QRH Runaway Stabilizer which is Control column...Hold firmly. Stab Trim Cutout switches....Cutout.
Meanwhile the nose is rearing up under full thrust. The mind boggles at the scenario