Seeking out guidance from a Professor at another institute during PhD I'm interested in the research of a particular professor at University 1 (top 5 in my field), which recently rejected my PhD application. I do have an offer from another place, (University 2, top 20) which I now plan on attending. 


Can I go to University 2, complete the requirements for a masters, and reapply to University 1?
Would it be possible for me to seek out guidance from (or maybe even collaborate with) the professor at University 1 during these two years who might then want me as a PhD student? 


This is all in the US.
Of course you can, and this is probably your best chance to make it into U1 (without any guarantee, clearly), but this involves a risk of straining relationships to your supervisor at U2.
This is a question you should discuss with your supervisor at U2 (after all he/she should give you guidance as well and careful argumentation is needed to explain why extra guidance might be appropriate), but don't be surprised if the professor at U1 would not be seeing a collaboration with you as a priority -- he/she might be busy enough with all the commitments towards his own institution.


Doing what you suggest is all within your legal rights, but I personally think when you have entered an agreement at U2 (possibly involving funding) then you should focus on that and not give the impression that you want to run away at the earliest opportunity.