Both Steam Controller and Xbox 360 controllers?

I have a wireless XBox 360 controller receiver that works just fine with Xubuntu 16.04. I can use it with two XBox 360 controllers without problems.

Since Father's Day, I also have a Steam Controller, and I've gotten that working just fine as well. (Indeed, it was much more of a pain to set up with Windows.)

However, I can't really use both at once. When both the Steam Controller dongle and the XBox 360 wireless receiver are plugged in, the Xbox 360 controllers seem to be registered as the "first" controllers. The Steam Controller works in Steam itself, but when I try to launch a game, the games detect the XBox controllers and don't respond to the Steam Controller.

So, the only way I can use the Steam Controller is to unplug the XBox wireless receiver. It'd be nice to have the XBox controllers available for multiplayer games, but have the 'default' controller be the Steam Controller. Is there a way to arrange this?