When I solve a 4x4x4, I always enjoy building a 3x3x4 first. The way I typically do it is:
1. Build opposite centers
2. Build a 1x3x4 Block on L using one of the completed centers
3. Build D center
4. Match and place 4 edge-center-center triplets for F and B
You might notice that step 1 and 2 are the same first two steps of k4. k4 then moves on to solve all the centers where here I try to solve two dedges as well. I have also read about people using a similar technique but a little more structured. They build layers in order from left to right instead of building both simultaneously. Step 4 might seem odd, but it can be surprisingly fluid. It's all about the look-ahead. Also, I could really see step 3 and 4 being combined without too much effort.
Anywho, I really like the 3x3x4. There are a few different ways one can proceed from here: finish reduction, solve last slice/cll/ell, etc. My best times with this technique are sub 1:20 (set almost a year and a half ago), but I almost never practice. Hope that helps.