The first question I have is, Why 35mm? Do you own a projector and theater? How and where do you expect to show these prints, and for whom? Why 35mm instead of DVD? What kind of films are you looking for?
I believe there is a small community of collectors of 35mm prints (hell, there are collectors of everything you can possibly imagine), so you might try to connect with them, although I have no advice as to how to do so.
But I believe that, technically speaking, it is probably not possible for an individual to legally own a 35mm print of any film that is not in the public domain. And the number of major Hollywood films in the public domain is very small in relation to the number that aren’t.
Prints made for theatrical exhibition are leased (not sold) to theaters. After appearing in first- and second-run theaters in North America, most are shipped off to theaters overseas. I don’t know what actually happens to them at the end of their lives, but I’m pretty sure that the official line is that they are destroyed. Even if you were able somehow to cadge a print from some Asian theater, it would be in pretty bad shape by that point. But the point is that prints always remain the property of the distributor, and AFAIK are never sold outright. So your Asian print would be stolen property.
Mainstream distributors have no process to deal with individuals, because the number of individuals who own 35mm projectors is vanishingly small. I’d be very surprised if you find any distributors that are willing to talk to you. And they just won’t sell you a print outright.
(BTW, if they did, the price for a new, two-hour 35mm print would be about $2,500.)
However, it is possible to rent films legally for non-theatrical exhibition. Swank Motion Pictures is the top non-theatrical distributor of films, making DVDs, 16mm, and 35mm prints available to colleges, film societies, churches, etc. They (and a handful of other non-theatrical distributors – see the list on this page) are probably your best, if not only, option for getting a 35mm print of a major Hollywood film.
The last time I did this was in 1984, when I was the head of my college film club, but if things haven’t changed much, your agreement with Swank (or whoever), will specify a certain number of shows on specific dates, with a payment based on the number of admissions. You will not be permitted to advertise the screenings in any mass media (TV, radio, newspapers, etc.), and will have to return the print promptly at the end of the run.
I hope this is helpful.