Data integration is by no means a solved issue, I know of people working on frameworks to try and answer the kind of question you're asking, it's just a very hard problem. Scale of data, technical noise, annotation links between experiments, i.e. how can you show that transcript / gene / region X is linked to metabolite Y? You could take an agnostic approach and test everything against everything in a pairwise data type fashion, eQTL-esque I guess, but you'd have to design that test from scratch, and know each datatype very well.
Overall there aren't many ways to throw three data types from different experiments together and just come up with a magic P value that says region A in transcriptomics, metabolite B, and Protein C are linked in some way, there has to be a more specific hypothesis, and you have to have a rough idea how the data types fit together, the classic example being methylation and mRNA expression.
ARACNE may be a starting point, I've heard of a few people using this for "systems biology integration", overlaying networks, but I can't offer any first hand experience on that front.