No, the information in the additional variables would be like a hidden variable theory, but the hidden variables make predictions that disagree with the experiments https://en.wikipedia.org/wiki/Hidden-variable_theory
There are a few physics theories that use additional dimensions, but they are use quantum mechanics.
Interesting. Can you confirm my ELI5 understanding of it? Is it that we could potentially claim that QM is not really random, we simply do not have all the data (like predicting a dice roll without accounting for the roughness of the surface). But then, experimental evidence contradicts this claim. Correct?
There are a few physics theories that use additional dimensions, but they are use quantum mechanics.