Air Pass through grate question..

[Kamori]

I had a wood burner installed in the lowest level of my house this past fall. My house is a traditional tri-level home with 4 mini flights of steps. The stove is in the lowest corner of the house. It worked great all winter heating the entire house, but in the lowest level where the burner is, it was so darn hot. I was wondering if code allowed me to cut a hole in the ceiling directly above the wood stove and just attach a "banister" (pass through grate) to let the air pass through the lowest level up the the 2nd highest level. Is this safe to do and also do you think it would be an effective way to get the heat upstairs quicker in return making the lowest level not as hot as it was? Any info would be great.