Probably not, it is possible with the original Java class, but the Processing wrapping isn't as flexible. Idem for file filters, etc.

Thanks PhiLho, what would be that class? Any known example?

Look at the implementation of selectInput() in the source of PApplet. It can be used as a start, and look at the Oracle API to see how to add parameters to this.
Search the class from Processing.org, you should be able to find examples of usage in the old forum.

Great! Thanks! I'll do that.