There are many reasons as to why I would not house them together.
First, they are more likely to stress as these are not social creatures in the wild, they are solitary. Second, you also run the risk of if any get sick, passing it around to the other burms. It's also really hard to tell who has defecated in the cage for reliable record keeping.
You are not only dodging one feeding response when handling, but (three?) more than that and this could not only lead to your safety being sacrificed, but their's as well if one decides the other one moving in front is food because it smells food in the room or any other reason.
If I've forgotten anything, anyone please feel free to add in. 
Just my $0.02. You're just ultimately better off housing them alone.
Hugs!
Amanda Rose