I will add one slightly off topic but I think relevant observation:
I never really liked pt pd prints as I am first a Silver printer, the dmax of any straight pt pd print is lacking IMO. But I love adding colour and depth to silver prints and toning for me is a decent method but nothing like separation negatives to add gum coloured tonal areas.
Irving Penn tried to wrap around this by various means, I have had the pleasure at my shop seeing in my hand a PT PD by Irving Penn of Luke 56 the hells angel series. Since I was not present at the printing I can only guess from my own testing is that the negative that eventually was made was super contrasty to give dead and I mean dead blacks which in my eyes lacked any shadow detail. It amazes me that he never tried multiple gum over Pt Pd like Edward Steichen did with moonrise over Lilly pond and the Fliariton Building in New York.

I have found a few benefits from printing gum over palladium that are relevant to this topic. I use a shadow separation negative to print in register overtop of a Palladium coating. The pigment I use is a mixture that is complimentary colour to the tone of the Palladium thus creating when combined a deeper black, I do not allow the pigment to enter any other area than the shadows and if I want to I can do multiple coats . A second benefit is that by using a layered gum process the print itself thickens and has a nice texture that IMO mimics adding a waxing.
The over all benefits are, deeper blacks that still maintain good shadow separation, great highlight upper midtone detail from the Pd, the ability to add colour where I want and the calmative effect of layered gum (tree sap) over the image.