If you add more, it will get dirty even faster.
Personally, I would not add more chickens in that amount of space.
One common guideline is 4 square feet per chicken. That would allow 30 chickens, so your 39 would be "too many."
I've also seen a guideline of 4 square feet each for dual purpose chickens, 3 square feet each for Leghorn-types, and 2 square feet each for bantams. With 16 Leghorns, 4 bantams, and 19 dual purpose, you would still have "too many," although not by as much.
As you've noticed, "too many" does not guarantee problems, but it certainly does increase the cleaning! And problems like pecking and bullying are more likely to happen.
I would suggest you choose a target number of chickens, and not get any more until enough chickens have died that you have "too few."
Based on your comment about cleaning last winter, and the size of your coop, I would suggest a target of 30. (Maybe let it drop as low as 25, then buy enough new chicks to bring it up to 32, then wait until it next drops to 25...)