My approach would be to use the STRING app to retrieve a STRING network for the two diseases from within Cytoscape. I would then color the proteins by disease and use clusterMaker2 app to run MCL clustering on the network. After that I would look at the network to decide some criteria for picking clusters involved in both diseases, Once that is done, you can do an enrichment analysis of the proteins in each such cluster using whichever enrichment tool you prefer (within Cytoscape or outside of it).
However, as i wrote in my reply to your previous question, I would probably not even do the enrichment analysis. The modules themselves may well be a better description of the functional connection between the two diseases than the terms that would come out of an enrichment analysis.
If you want an idea of how the result can look, I put together this poster last week, using the approach described above.