For what it's worth, people have compiled a list of every single movie that received any vote in the most recent sight and sound poll (combining directors and critics, I think). Technically every single movie was in
someone's top 10 greatest films of all time. That list is over
4000 movies (looks like 4420 of them).
And these lists are usually still just supposed to be launching points and not comprehensive (While I probably wouldn't classify all 4420 of those as "masterpieces," though it's not really clear what the term should mean to someone, I can think of other movies that I would think should be considered in the same level/categorization as those. And there are vast gaps of ignorance on my part of films I've never seen (can I even name a Bengali film not directed by Satyajit Ray? I cannot) that would probably yield a large number more. What I'm saying is, yeah, probably 10,000).
I think how you define masterpiece (which is subjective) is a factor, as well as your subjective opinion of particular films.
I was doing it largely on instinct when I came up with my 136, but off the top of my head, I was almost without exception (although there are a couple of exceptions) looking for something visually stunning, and also first rate acting. Ideally I wanted something which also moved the art of cinema on in some way, or in a handful of cases I settled for what I saw as the best example of a particular genre. And on top of that I needed a great immersive experience, a film that grabs you and pulls you in and has something truly exceptional about it.
Of the first 100 in that list you've linked, I am familiar with 91, and only included I think 31. A large number of others in there I actively considered but chose not to include. And that seems to be the highest ranked/most voted for 100 films.
I think that if you have the extremely restricted criteria I had, then it is just about possible to identify a list of masterpieces. Once you drop the requirements though it does become an impossibility with probably thousands, including goodness knows how many you have never heard of, being eligible.
It's interesting by the way that whilst I recognise that a couple of comments such as "42" etc are likely facetious, there do seem to be 3 broad schools of thought on the thread:
-c50-c150
-c200-c500
-several thousand/10,000+