Razor wire on the American side would be a good idea along with the fence. They would think twice about climbing the fence.
I just did the math on the estimated $6B to build the first 854 miles of fence.
That is 854miles * 5,280ft/mile = 4.5 million feet, which means over $1,300 per foot of fence.
You can string a 6 coil pyramid of razorwire for $20 per foot, and have it done in a week, while the fence crews follow at their slower pace.