A sudden transient load, provided it is very short, may be overcome by fitting some large energy storage capacitors across either the dc input to the supply, or across the particular dc output that is being loaded.
Which is more preferable will depend on the relative dc voltages involved.
Stored energy is proportional to voltage squared, so for any given total capacitance, the energy storage capacity will work much more effectively if carried out at a higher voltage.
As you mention the input voltage drops by 20v, I am assuming the normal input dc voltage is quite high, so that may be the best place to fit some suitably sized electrolytics.
An alternative strategy might be some ultra capacitors at the dc output.
Either solution is worth looking into, particularly the relative costs.