A few things that work very well for me:
I only take the lead stuff (melodies) from the source track and forget about the rest (e.g. chord progressions, basslines, etc.).
Up-front I usually already have an idea for the genre/style I want to do, and I usually try to push myself to try new things and make the genre different from what the source track uses (e.g. make an orchestral Megaman track in stead of a more stereotypical rock arrangement)
Arrangement structure is flexible; why stick with the exact structure that the source uses? No problem in turning the B section into a verse section, the C version into a chorus and use the A section as a solo, for example. In general, I write like 8-16 bars and then think "okay, I can either go more intense or less intense from here", make a judgement call based on that, and just run with it. Try to make it an organic part of your process and just treat it as an original, I guess (there's a reason I call my remixes "originals with stolen melodies").
Hope this helps some.