Well heres the only other ones I'm willing to share at this time
Number 1; The Lutece Twins come up with some mental switch-a-roo with the current Alpha and his counterpart in one of the bioshock verses as they desired to pull a kind of test that if successful would provide double the entertainment as you could easily imagination the chaos it would cause.
Number 2 . the Lutece Twins are displeased at the turn out of what was a enjoyable reality they stumbled upon(The first Alpha's earth) and choose to try changing a almost identical worlds fate which started Omegas none Indrain dimension/world and time traveling endeavors
Number 3: The Lutece Twins was growing tired of the endless cycles of Alphas that to them was like a combination of reruns and reboots depending on the world/dimension they are viewing. So they desired to spice things up via trying to drive Alpha insane or have Alpha seem insane enough to be put in a place for mentally off beings as a way to change it up but they always was making sure Alpha would get out or atleast be changed to a place that interesting things would still happen
Oh and if you watch this
https://www.youtube.com/watch?v=2P81NLAtjjs skip to about 1:08 and listen as you watch it made me laugh when I found it