Attending a CFAR workshop and session on Bayes (the 'advanced' session) helped me understand a lot of things in an intuitive way. Reading some online stuff to get intuitions about how Bayes' theorem and probability mass work was helpful too. I took an advanced stats course right after doing these things, and ended up learning all the math correctly, and it solidified my intuitions in a really nice way. (Other students didn't seem to have as good a time without those intuitions.) So that might be a good order to do things in.
Some multidimensional calc might be helpful, but other than that, I think you don't need too much other math to support learning more probability and stats.