I cannot seem to find any concrete answer in the PHB for this, so I ask away.
Can multiple instances of the same spell stack if they provide a different effect? An example being can one be affected by both a resist energy spell for fire and a resist energy spell for acid? Would this apply to a spell such a "spell immunity" as well?
I believe the answer is yes in this particular case. You cannot stack multiple benefits from the same source in any instance, but nothing is stopping you from having multiple benefits from multiple castings of the same spell to different stats.
Nothing stops you from having multiple castings of the SAME variation i.e. Resist Fire (or for that matter, any other spell, like Enlarge). They won't "stack" (augment effect) since they all do the exact same thing and there is no mechanic for additive Resistance stacking, but if one gets dispelled etc, the other(s) would still remain. Nothing says "target becomes immune to further castings for the duration".
If you have multiple casting of DIFFERENT variations of the same base spell, those also can be cast on same character simultaneously, and their different resistances will usually apply to different effects/attacks, except VS multi-type damage effect/attack which could possibly trigger them all. I used to think you only used the single highest Resistance VS one effect/attack, but AFAIK that isn't true: if suffering X type damage, you apply X Resistance (and if suffering XYZ type damage, you apply XYZ Resistance).