I think I know what you're trying to do and there are several ways to do it.

If I understand what you're trying to do correctly and where you're hung up at what you may not have done is combine you're several smaller polygon meshes into one BIG mesh. That may be why you can't sew the UV's together. Technically they're not the same mesh. You could select them all and go to Mesh --> combine. But you'll have to go in and line up vertices and merge them so they come out nice and neat. Then you can go and make your UV maps for the big mesh.

OR

What I would do is take the original three steps you created and unwrap those three so you have a map. After you have those three mapped out you can duplicate them to make the rest of the stairs and all of the duplicates will automatically have the map laid out like the originals. Then when it comes time to finish the map you can just move everything about until you have it laid out like you want without having to unwrap each single step.

Hope this helps!