No. There isn't. You can only request one key during the giveaway period, and once that's done you're locked out. The only other way would be to trade keys with someone else.
Requested The Darkness Among Us DLC from giveaway - Wrong Key given
I requested a key for The Darkness Among Us DLC which has just gone live and the key I actually received was Descend Beyond. Now I know that it's a still a DLC, but it's not what I had actually requested and despite it being free content I kind of feel let down by misadvertising. Is there any way for me to actually get the correct dlc?