It seems like there could be a lowest-common-denominator set of phonemes that such a system could be built on, with translations into symbol groups for different languages. As long as those symbol groups are relatable by two people who speak the same language, that might be sufficient?

Or just offer different sets of phonemes for different languages (and allow easy switching). You don't need any commonality across languages.

Of course that's not helpful when two people who don't speak a common language are trying to establish communication, but it probably isn't their biggest problem.

>> "lowest-common-denominator set of phonemes"

They already spent a bunch of time and effort finding these phonemes to build Esperanto, right?

No, see this criticism of Esperanto phonemes: http://www.xibalba.demon.co.uk/jbr/ranto/#b

Its choices are large, irregular, unclearly defined and basically Eastern Polish.

Esperanto was designed to be partially understandable by people across Europe by lifting words from various languages liberally.

Lojban is designed to be well-defined on phonemes, but that still only works when knowing its (rather simple) pronunciation rules.

That would probably still be a very eurocentric set of phonemes, so probably would not really be suitable for the modern multilingual world, I would think.