Heat 2 TB olive oil in a large skillet over medium-high heat. Cook the sausage and onions together until sausage is browned and onions are soft. Transfer to a plate and set aside.
Reduce heat to medium and add remaining 2 TB olive oil to the pan. Add zucchini, yellow squash, bell peppers, mushrooms, and garlic and sauté until softened, about 5-10 minutes.