When people hear the words "stability" and "stabilization," many think "midline." This is because we drill the concept into your head during class - midline stabilization is essential for safe and efficient movement. But do you ever think about stability as it applies up and down stream from your midline?
What do you do, for example for lower body stabilization? You might think squats, deadlifts, and Olympic lifting are enough - but I would argue that it these are only a starting point - a great one, but still just a start. Think about it - how many sports (or even daily activities are done with two feet on the ground at all times? Even the most foundational human movements (walking and running) are single leg activities. So how can only training two leg training be sufficient?
Working your lower body stability means adding single leg movements. These movements force you to stabilize differently, utilizing relying more on different muscle groups than in two legged movements. This allows you to better recruit these muscles when doing one and two legged movements alike and will help you become not only more powerful, but more efficient and less prone to injury.
Remember, single leg movements don't have to limited to single leg squats (expect to see those this month). There are many variations on single leg squats, Bulgarian squats, lunges, Romanian deadlifts, and step ups that can help you work your stability and single leg strength. Here is a good list of pistol variations in this CrossFit Journal article to get you started.