How to stabilize the aircraft flight after dropping boosters?
The most important aspect is the vertical distance between the booster's thrust vector and the center of gravity. Once the booster stops working or is dropped, a pitch trim change will be needed to compensate for the upset in the pitching moment balance.

Next, the horizontal distance between the boosters and the center of gravity will tell you how much the pitching moment is changed upon dropping the boosters.

If control authority is sufficient to trim all those pitching moment changes, stabilization should not be much of an issue, especially if a sufficiently sized tail gives sufficient pitch damping.