The answer I've commonly seen is that the most recent one will be the only one in effect.
Same Effect with Differing Results
The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
This is the main reason given... additionally there are spells that have a line in their description specifically to override this rule, whereas Energy Immunity does not.
I don't think that particular stacking rule is meant to apply to things like energy immunity
. The SRD leaves out an important clarifying example from the PHB:
Same Effect with Differing Results: The same spell can sometimes produce varying effects if applied to the same recipient more than once. For example, a series of polymorph spells might turn a creature into a mouse, a lion, and then a snail. In this case, the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
Emphasis mine. The example makes it clear that when the rules talk about one effect "trumping" the other they mean a scenario where the second spell actually cannot combine
with the former (i.e. you can't polymorph into a mouse-lion-snail hybrid by casting multiple polymorph
s in sequence), and when it talks about effects "becoming irrelevant" it means things like polymorphing
into a lion turns you into a lion no matter what form you had before rather than a hybrid of a lion and your previous form. Multiple energy immunities
aren't incompatible with each other in that way, since it's perfectly fine to have multiple immunities at once, so this stacking rule would not apply to it, and thus it wouldn't need to have any clarifying text overriding anything.
Likewise, it doesn't hit any of the other no-stacking clauses: it doesn't grant a bonus or penalty, named or otherwise; energy immunity (fire)
doesn't grant a "stronger immunity" (whatever that would mean) than energy immunity (cold)
(and the example makes it clear it's talking about things like a -4 Str penalty vs. a -6 Str penalty, the exact same effect); neither renders the other irrelevant, since as mentioned multiple immunities are entirely possible.
As far as I can tell, you should be able to benefit from two, three, or more energy immunity
spells protecting against different energy types.