Fixing additional layer of plasterboard to an existing separating  wall will likely yield some improved performance. However the amount of gain will be dependent on the specification of the original wall. As this is already a high performing wall (fire and acoustics) the increase in performance may not be that significant.

To best advise, the specification of the existing wall would be required and an understanding of the uplift in performance  desired. Options then can be considered with an estimate of performance gain.

The additional layer will need to be mechanically fixed back to the studs in the partition (whether timber or metal) as per Siniat guidance.

If the party wall is a blockwork with plaster finish the Dryliner system should be considered:

For walls already lined with the Gyspum bond system, this should be removed first then a new framed system installed. An independant lining system can be installed in front of the "Dot n Dab" lining but the amount of space lost could be prohibitive.