You'll probably get a huge range of opinions - but I'll give mine...
I've had several pairs of skis where the previous mounts interfered with the desired mount holes. (Like the holes actually touched.)
(I haven't had one, that I recall with 3+ mounts on it, but I'm not sure that matters a ton. But I say this in the spirit of full disclosure.)
All the skis I have experience doing this with were all very burly skis - most with two sheets of metal.
I have simply moved, in all cases, interference or not, to plugging old holes with bamboo skewers and epoxy. (And a little more on top to seal the plugs, BTW)
Then I simply mount wherever I desire. In a few cases, the new holes touch the old ones, and I've never had a mount rip out.
IMO, if you fill the holes, and use epoxy, I think the core is likely to be very nearly as strong as before.
(Or you might die, I dunno...) :)
[Edited to add: So, to be clear, if it were me, I'd pull all those plastic plugs, (drill the centers out with a small drill, insert a small #4 or so screw, and yank with a hammer nail-puller) then plug them with skewers and epoxy, and mount where you want. If it made me a little more comfortable, I might adjust forward/backward mount a little to add more separation.]
My minimal-worth $0.02.
-Greg