Some info is the speed of the paper
Buried in Ilford, Agfa, and I thing Kodak's pagakging of B&W paper are little leaflets that tell you about contrast ranges in the negative that correspond to the multgrade filter for that denisty, and usually in that table there is a suggestion of the relative speed of the paper under raw white light, as well as under the filtered light.
I believe there is even a scale on an old kodak darkroom dataguide that I have that helps out in switching between papers. I don't recall what the units are called. It is on the inside if the scale that I usually use to calculate new exposure times when raising the enlarger head after making a modest sized good test print.
I do recall that Ilford MGIV is something like 400 under white light, while Agfa MG?? 111 is like 250, i.e it overall needs 400/250 worth of the Ilford light to produce the same level of blacks
The adjusting of filtration might be discernable from the contrast rnage data, but I think that there will still be some trial and error work reuired when swapping papers.