Controller and driver for 3 stepper motors

Can Ardinou drive 4 stepper motors at same time?

Arduino and stepper motor controllers

Yes it can. You either need to choose a shield which can drive four stepper motors, two pairs of dual stepper motor shields whose pins do not overlap, or external stepper controllers (I2C for example allows you to assign addresses to each and uses only two IO pins): https://www.robotshop.com/en/stepper-motor-controllers.html