I have a situation where ideally, I would like to resistance spot weld three rather than the usual two plates together (individual plate thickness approximately 0.7mm). Is this at all possible? If not, why not? Are there any precautions one should take?
Yes, as per comment, but you have to check current density to make sure sufficient temperature is achieved otherwise the bond between some layers becomes weak.
Making, welding then testing several examples with variations of parameters is usually the way to proceed.