Decks, Patios, Porches and Docks - New step on existing patio

When my house was built the patio was poured with a single step up into the house. The concrete sub. did a sloppy job on the step itself. It's too narrow, too short (not too much),and with too great of a slope. Rather than break the original step up (without damaging the patio) or trying to pour a new one over it, I thought building a step out of treated lumber would be easier and look better. What do you guys think? It could be built larger than the existing step and fit over and around it. Attached to the side of the house with brackets to make it removable if I even needed to.

It can be done, but think it through thoroughly.

The rise from your slab to the tread of the step has to be the same as the rise from the tread of the step to the threshold of the door. It's probably already there, so you can't deck over the step (or stoop). That will create too much variation in the rises.

One option would be to leave the top of the concrete step exposed and deck around it with wood or a composite. But "too much slope" could present problems.

The better option would be to rent a roto hammer or 60 lb. jack hammer and take the top of the step off (3" or so) and simply pour a new step. (A roto hammer is MUCH more user friendly!!)

I've thought about that too.
How would I keep the fresh concrete from squeezing out from under the form? Even if I have the form perfectly shaped to the patio I think it would seep out. Would I need some expansion material between the house wall and the new step? There isn't any now, the step is just pour against the siding.
What about anchoring the new step to the old patio?
Would I need wire mesh or some kind of rebar in the new step?