A trick I use to change brightness characteristics of inkjet paper is to print a base tone on the paper before I print the photograph. This allows me to get exactly what I’m looking for when it comes to brightness.
I mainly do this technique with cover stocks for artists’ books. For my photos I just use standard papers. There are more than enough single sided papers to fit my needs. When it comes to book printing, sometimes what I need for a DUO cover stock is not made in the brightness / color I want. (Cream, Ivory, light blue or rose.)
Tints can be adjusted infinity in Lightroom, so it is easy to make an encyclopedic collection of hundreds of tints. When doing tests realize that tints show up differently on matte and gloss papers, so you will have to adjust the tint depending on the surface of the paper.
Some papers take double printing poorly, so test it out before you go into full scale production. If your using a gloss enhancer, you will most likely need to shut it off when printing the base coat.