While the local Colora Nostra seems fond of having a profile for every media, I have found after 20 years of printing on all manner of media that it's really not necessary at all. In this shop there's exactly two, count 'em two, profiles. One for vinyl, canvas, banners, and everything else save paper. Paper has its own special profile. The base profile for both of these are Oracal's profile for 3651G from many years ago. This profile was tweaked some so that it printed satisfactorily on most everything, even silver metallic. The paper profile is the same but with the ink levels turned down a bit. One added benefit to doing it this way is that it makes the local chapter of the Colora Nostra go to the mattresses Most amusing. They will wail, wave their arms, and insist that this cannot perform optimally. To which I respond that medial printed with its own special profile and the same media printed my way are functionally indistinguishable. I'm not trying for 'optimal', I'm going for 'saleable'.
What are those tweaks? Just a few, set the dither algorithm to the highest quality available and set the rendering intents to "No Color Correction" for everything except bitmaps which is set to "Perceptual". Then always input bitmaps in RGB at 150 PPI or so and the printer to output at 720 DPI or so. You want the output resolution to be ~ 4x the input resolution. There may be a few more but those are the main ones.