Her back throw is not as good for throwing people offstage as it was in Melee, and her down throw can't guarantee a chaingrab. Instead, her chaingrabs relies on DI traps. Because of this she has the ability to Chaingrab almost anyone who is not a fast faller. It just takes a bit more thinking than usual
Say you down throw an opponent and they DI away not allowing for another grab. The next grab you do, you might think "He's going to DI away, let me back throw him instead." You bthrow instead of dthrow, and you were right, he was going to DI away, so now with the bthrow, his away DI turns into DI toward you and pops up into the air, allowing for a regrab.
You now must think again, will he DI away this time to DI the dthrow? Or DI toward and read the bthrow and therefore DI away. Say you keep guessing correctly everytime, you're chaingrabbibg him now.
If he can't correctly guess the throw you are about to do you can follow up accordingly. If he screws up the bthrow DI you can follow up with a fair when he pops up and enter an edgeguarding situation. And the good thing about the bthrow if they do correctly guess the DI and you're near the edge, you can still enter an edgeguarding situation, as they will be offstage now.
There is also the DACUS, which maybe you can follow up after a dthrow? I haven't tested it, yet. It might work.