Acceptable voltage spikes
2V to 3V spike is probably not acceptable. A spike that big can disrupt operation if it gets into a reset line, interrupt line, clock line.

You can come up with an acceptable spec for the spike amplitude. Go through your circuit, identify important voltage thresholds: digital thresholds, brownout voltages, maximum supply voltages.  (O.P. doesn't mention any analog circuitry, so I'll leave that out.)  That will tell you the amplitude of the spike which your circuit can tolerate at one place or another.

A typical microcontroller circuit running off +5V usually can tolerate a 0.5Vpp spike.   But please treat this just as a hand-wavy guess, which is good only for providing a starting point.

Usually, the best place to attack EMI is at the source.