There are some aspects to consider:
(i) the ski construction
A ski with titanal upper sheet would probably survive more holes
(ii) the use of the ski
A ski used on groomers takes much less stress than in bumps or in similar conditions
(iii) the location of the holes
Holes weakening the ski in most critical parts (ends of the plate or toe/heel of the binding) are worse than those in the middle under the boot sole. Holes accumulated there with only around the minimum distance from each other may be critical.
Sometimes it´s surprising how many holes a ski can take. I tested various plates on a pair of skis for a Czech manufactuter. The skis finally had almost 40 holes each and I had to use a sophisticated systems of marks indicating which holes belonged to a particular plate.
The ski finally for some unexpected reasons even took part in an international ski test in a short skis category (was 138cm long) and got the highest 5 stars evaluation - riddled as described...
(The skis were very stiff and the holes even might have helped them to flex better...
. As a method not to be recommended, though.)
There are special plastic plugs to fill the holes with, preferably used with some glue. For skis with wooden core wood plugs with epoxy could be even better. The glue also prevents water getting inside.