Feasibility of enrollments in a Masters program at one university and a PhD program in another university
Maybe, but why? Different topics? 

In any case, you'd have to check the rules of both universities. 

As a supervisor/employer of PhD students, I would not want my student doing this. A PhD is a full-time job, requiring full-time commitment. Financing is scarce and I wouldn't want to waste it on someone who is not fully committed.