People who ask this question invariably under-specify the question. They just say, "How can I increase the number of files I can open at a time?" without saying how they're opening them. From the operating system's point of view, the number of files you can open at a time is limited only by available resources. Call
CreateFile until you drop. (This remark applies to local files. When you talk over the network, things get weirder.)
The fact that these people are asking the question, however, indicates that they're not using
CreateFile to open the files. They're using some other intermediate layer, and it's that layer that is imposing some sort of limit. You'll have to investigate that layer to see what you can do about raising the limit.
[Raymond is currently away; this message was pre-recorded.]