I can add to this that I knew technicians who would remove the loose
pin and then hammer it back in with a strip of veneer around it.
I have seen this work and I have also seen this not work.  I personally
would never do it like that unless in an emergency.

I must also add that I once repinned a grand piano that had very loose
pins.  I drilled it to the correct undersize and all.  It was fine for
about a month and then heaps of the pins were loose again.  Fifteen
years later I still don't know why, but I suspect there was something
in the wood from previous repairs that must have dried up or shrunk.

Regards,
Bernt Damm
Sydney