I understand space is tight by the front door inside the house, but it's very nearly as tight outside as well. The small space gained doesn't seem worth it.

What you could consider is:

1. Outswing door (unless you are in a cold climate) http://www.mcgarryandmadsen.com/inspection/Blog/Entries/2017/1/8_Should_a_front_door_open_in_or_out.html    Check local fire codes. This idea works best if most traffic on your side path will be headed away from the open door

2. Remove everything from that entry landing and set up drop zones at top of the upper flight and bottom of the lower flight

3. If shoes are coming off right at the front door to protect cleanliness of carpet on steps, I'd change the household policy and possibly also the carpeting, to either hard surface or a dark, dirt hiding flat weave.

Good luck!

You probably can't build out. Most areas have rules on how close to the property line you can build. If your fence is the property line then your house is probably at its max on how wide it can be.