It's not impossible to use a Black HAT for this purpose but connecting more than one add-on board is not exactly what it was designed for.
There are 3 sets of header pins 2x20, if you elevate the middle one then you could attach the Sense HAT there and your other board on the one normally meant to host the add-on board (the side towards the writing).
That said it depends on the physical presentation of your IR and its exact position.