Is the step surface itself moving or the riser/supports? Either way, the answer may be the use of a brad nailer--a nail gun that uses small brads that don't really leave a visible mark where they go in.
Our steps are 10 years old and have never moved, so haven't looked hard at how they are put together.
Let us know what you do to fix it.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired