Well, the guys from Holland did it with a Quintezz, for better warning against weak photo radar
here.
Generally, a physically larger horn will give you more gain. But, it's a double-edged sword, because it will also make the antenna more directional, meaning that it woukd receive fewer reflections from objects that are off-axis, which might end up hurting performance for over-the-hill or around-the-curve threats.
Be careful: without some methodical approach, you could very easily end up hurting performance instead of helping. Simply extending the existing horn with aluminum foil might change the antenna "plot" for the worse.
Jim