Adding a aftermarket strut bar might be the best idea

An aftermarket strut bar is a upgradable performance component that is designed to improve the handling of a vehicle by increasing the stiffness of the front suspension system. It is typically installed on the front of a vehicle and connects the left and right strut towers, which are the structural components that braces the front suspension. Under heavy loads typically endured during hard cornering on the track, the strut towers have a tendency to flex adding some variability to the suspension geometry and feel. 

Adding an aftermarket strut tower bar to the GR86 can help to improve the responsiveness of the suspension. When the front suspension is under load, such as during cornering, the strut towers can flex and cause the suspension to feel less precise and responsive. An aftermarket strut bar helps to reduce this flexing by increasing the stiffness of the strut towers, which can improve the suspension's ability to respond to inputs and provide a more precise and controlled ride

Overall, an aftermarket strut bar can be a valuable addition to an GR86, especially if you are looking to improve the handling and stability of your vehicle. Just keep in mind that it may also slightly stiffen the ride, so it may not be suitable for everyone. Here at GR Performance Parts we stock many different brands of strut tower bars for not only the GR86 but the Supra and GR Corolla!