Is there any way to snap one object’s mesh to another, without overlapping them?
I have several floor sets made and I want to continue extending them, but I keep having
to manually go in and carefully position it exactly next to the previous. I’ve looked through the snap options and none of them seem to fix my issue. Thanks

You can use grid snap feature and set size to dimension of your module for easy positioning.

Perhaps this link will help: Unreal Engine 4 (UE4.15) Tip : Vertex Snapping - YouTube