I think the term there is "arrangement", though. Yes, there are a lot of ways to play with harmonies, and with suspensions, anticipations, bridges, secondary dominants, and every other aural "trick" in the book, you can do whatever you'd like to make it your own...

BUT, to take a I-V-IV-II progression, and rewite it into a I-vii-V-v, can have ugly results, especially if the "arranger" in question unknowingly leaves a melody tracing the original chord structure.

A great way to practice, using Ted's suggestion, is to go pick up any one of Bach's four part piano pieces, and try it, to see if you can spot the "trends" that invariably come up. Baroque is very precise in its meter, and tends to be very simple in its structure. You can stare at four part 8th notes, reduce them down to quarter notes (look at how each voice tends to work around its "chord", you'll see R-3-5-3-R-6-4-R in one bar, in one voice, and realize "Hey, the first four are obviously I, and the last four are obviously IV") and eventually spot the chord progression. The trends you'll see (and you'll recognize them in everything now)...:

I-IV-V-I (EX: Summertime Blues) I-IV-V-IV (EX: Louie, Louie) I-V-IV-V I-III-IV-V I-VI-V-VI

Just keep looking, keep playing, and always listen for what sounds good.