“The Overwhelming” is a bit, well, overwhelming. It’s a play with a scope so big and a subject so heavy it threatens to consume theatrical essentials like character and space. But nobody said doing a show about the Rwandan genocide would be easy.

Part political thriller, part cultural dialectic, part family drama, “The Overwhelming” has a lot to juggle. In its Boston premiere from Company One, J.T. Rogers’ play drops as many balls as it catches. But it’s hard to knock something that shines a spotlight on an atrocity that needs remembering.