What's hiding behind partial squats?
If you're trying to impress with your strength, that's all that's likely to happen. You will gain more strength and produce more testosterone and growth hormone with a full range of motion. Your body composition will be improved (man and woman).
If you think it will protect your knees, you're wrong. Several studies show a better adaptation of the hip and knee with a complete range of movement.
If you think it will protect your back, you're wrong. You should first be able to do a full squat with no charge, and only with your body weight and with the adequate form. You can then apply the progressive overload principle.
If your body leans too far forward when you squat, it's because the back of your hamstrings and buttocks are not strong enough to support the load and the psoas are rigid and cannot collaborate with the movement. This problem should be solved before thinking about increasing the load.