Ask the tree experts

It is possible, but not advised. The procedure is called crown reduction. Which is removing a branch to another branch that is at least a third of its diameter. A common side effect is "water sprouts". Which are multiple branches growing verticle near the cut. These can not be stopped and can potentially cause the tree to grow taller then if it was not trimmed at all. Crown reduction is not as devastating for trees as topping is but should still only be done as a last resort.