How to increase output voltage of an op amp well above the supply voltage
You’ve added a whole lot of gain and some phase shift, both of which negatively affect closed-loop stability, notwithstanding the internal compensation in the op-amp. How it is done depends on the requirements, frequency response and load driving capability in particular. Driving piezo actuators, for example, is more challenging because they are capacitive and add even more phase shift. 

Speaking of the op-amp, you are applying almost double the absolute maximum supply voltage of 5.5V to it, so it would likely fail instantly in real life.