I understand that you want to pass through walls and such, but have no idea why you refer to it as a phase. You mean like different phases of matter like he turns into a gas?
In the hard sf novel Pushing Ice a character from the near future is transported via a "travel cowl" from the far future, where nanotechnology is perfected. Shenis astonished how she got sevel levels and past several security doors, instantly. "In small pieces" was the reply.
More along the lines you're thinking of,
The particles in his body could be changed into something else, which have analogous properties relative to themselves. That is, atoms and molecules exist unchanged because the use of electric charge is changed to X charge in a uniform manner. But it won't interact with normal matter at all, so, he can pass through walls and would fall through the floor.
How about an envelope that changes the nature of space by fiddling with some parameters, and whats inside seems normal within but acts as explained above. Now how to selectively interact so can see, push against the floor, etc? It provides an interface layer that can be tuned to touch normal matter when needed. Recall that charge is not enough to be solid, but that has to do with being (exactly) electrons, so the envelope would need ro prodice an exposed layer of matter and somehow react with that in some other way.
E.g. the bottom of the shoe and anywhere touchnis desired is coated with a thin layer of room temperature superconductor. The envelope contracts to expose the conductor and manages to still stay connected rigidly woth it by using flux pinning and thus a pure electromagnetic effect that applies to anything with charge. The interface (on the inside of the envelope) produces a transition material that interacts (at half strength) with both the X force and the electric force. Superconductive currents of these intermediate particles (since only pure X-regime electrons touch in the normal manner) can be controlled with X-regime electrons and induce a charge in the normal superconductor, so flux pinning can keepmthe sandwich together.
The exposed material then interacts with matter in the normal way.
To get your shoe through the wall too, the envelope is extended to cover everything. This has to be orchestrated carefully to change the properties and the tuning of the mechanisms that hold it together. And that provides our Hero with (quite literally) his Achilles Heel. I think it would only be vulnerable when shifting, but if he's walking through a wall that needs more than one step to pass through, the shoe needs to turn On interaction whike still embedded inside matter, and thus not take up any room. Without going into how that might be done, note that the whole interface business uses superconductors and strong localized electromagnetic fields. What if the surrounding material interfered with that?
If the mechanism were compromised he would not only be unable to take a step but would not be supported by the floor and would fall into the earth never to return until he ran out of air or power.
If he passes through something that damages the interface but succeeds; e.g. jump through a thin wall and then turn it completely off before hitting the ground; it would render him crippled, only able to safely use the power by jumping while running at the wall and then turning it on.