Do you prune off crossing branches of a Red lace Maple?
It sounds like your tree has an excess of crossing branches! As you say, you cannot remove them all now or you would cut off half the tree. At this point, I would remove the branches that are most offensive, the worst crosses, step back and look at the tree. If you can remove a few more, do. Then next year remove the rest if possible. If that is too severe, do the rest the following year. The important result of removing crossing branches is to remove any that are rubbing. Some trees are naturally twiggy, and need thinning out, but the important issue is the rubbing.
It is best to prune Maples in the summer or very late spring when the leaves are out as Maples are spring bleeders—sap will flow out of the area of the cut. This is not very harmful to the tree but might attract insects. Pruning with the leaves out is harder, but prevents the bleeding issue.