I'm sure you have reasons for wanting more than 255 file handles open at once, but in a situation like this, I'd be more inclined to revisit and rework the app design. There's bound to be a way to divide the task into partitions or stages, so that you make the best possible use of limited available resources.

For example, if it's a job like sorting some massive, monolithic input stream into a thousand discrete output bins, do a first-pass sort that divides it into just, say, 40 bins, such that each of these could then be easily subdivided into 25 sets by a second-pass over those output files.