I don't think pili multigemini would be an issue. It seems to be something genetic.
Look how the hairs grow in Riken's artificial skin. Each follicle growing nice and separately from the one next to it:
If they were to re-inject the same area again, the new follicles would probably grow neatly in the space between.
Maybe there is a saturation point/limit to how many hairs can be in a given space, but we know that some people have 400+ hairs per 1cm2.
Now the very fact you would be enquiring to have your already hairy areas injected probably means you had density around 200 hairs per cm2 or more likely less than 140 per cm2.
Tsuji's method would boost the density up by about 130 new hairs. That would still mean you would be quite a bit under the 400 per cm2 found in some densely-haired individuals, who don't exhibit pili multigemini.