Obviously this institution could just make all its patents free for anyone to use. But it could also use them as a hammer to force open other patents.
For example, you could make all your patents absolutely free for any other institution who does not own any patents. If you do own any patents, then you cannot use our patents unless you also make your patents completely free under the same license. (sort of like GPL).
This might be too restrictive, but on the plus side if you just got some good patents into this institute, that would force lots of other people to open up theirs under the same license, and in the ideal world it would quickly snowball.
(of course this was the idea of GPL open source code as well, and I would say that has generally been a complete failure; the real result of the GPL is that nobody serious can use GPL code, so all the GPL libraries out there are just wasted).