It will be hard to generate any kind of power throwing on the same side like that. It would score points but not likely to finish anyone. Plus you're going to be off balance.
I worked this a little this morning and I kept following it with a rear leg high kick and it was scoring pretty well. I'm assuming that for you to do this consistently your kicks are better than mine so you shouldn't have a problem with that. You can always throw a body kick as well. All though it maybe more difficult then I think as one of my favorite kick combos is the low kick air switch to low kick.
If you wanted to be really fancy, you could throw a spinning wheel kick with your lead leg using the force of the foot sweep coming back to spin. I did that once when I got a really clean trip and had to pull off to avoid heel kicking my partner in the face.
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This. You want be throwing you strikes from alternate sides.