You can calculate that 3 motors requiring 3 A each require 3x3 = 9 amps. Even two motors would require 2x3 = 6 amps.
Your power supply is therefore only adequate to run one motor, making no other assumptions.
Sometimes stepper motor drivers are set up to use a lower holding current than their stepping current, so would use less when stationary. So the next step is to estimate, or simulate the operation of the machine, to see whether more than one motor is required to move at the same time.
If I was investing in replacing all three motors, I would replace the power supply as well, so that I could use all three motors at the same time.
Of course, being retired, I'm way behind the times. As Jack points out in comments, the drivers are probably switchers rather than the old fashioned linear types. With linear drivers, supply current is motor current. With switchers, supply power is motor power, and, as the motor voltage is usually a fraction of the supply voltage, supply current can be a fraction of the motor current. So, find out what your drivers are, you may be pleasantly surprised.