Combine broccoli, cauliflower, edamame, carrots, and water in a microwave-safe bowl. Cover with plastic wrap and microwave for 1 minute until vegetables are tender. Set aside.
Heat olive oil in a skillet over medium heat; add onion. Cook and stir until onion is softened and beginning to brown, about 10 minutes.
Stir cooked broccoli, cauliflower, edamame, carrots, zucchini, mushrooms, and garlic into the pan; cook and stir until vegetables are cooked through, about 5 minutes.
Stir in reduced-sodium teriyaki sauce and agave nectar; cook 5 more minutes.