This is commercial work? Then just ask your electrician. Amateurs aren't allowed to work on commercial buildings.

It's residential but in Chicago everything uses commercial standards, i.e. no one even sells Romex here. Everything is EMC/conductors.

I know what I'm proposing will work. What I'm asking is whether or not it's allowed.

I don't think homeowners are allowed to do electrical work on their homes in Chicago. So my comment probably still applies.

But as far as 'hypothetically speaking'? Check the box fill. I imagine the boxes on recessed lights are typically small. There are online box fill calculators that you can use. Just because you can physically stuff all of those wires into a box, it doesn't mean that you're allowed to.

This is a 6" can with a pretty large box. It's bigger than the double-gang boxes used throughout homes so there is plenty of room. You just can't access the box without removing the can but I guess that's no different than removing an externally mounted fixture.

If you can remove the can to get to the can's box, is there sufficient room to just put another box in the same vicinity accessed after removing the lighting trim? This should meet the accessibility requirement.

The can itself has a hard box as big as a double. Putting in another box unattached would definitely be considered a buried box. Plus, this is all conduit. I would have to run separate conduit both to and from.

If you can only access the box by removing the can, how do you plan on running emt from it?

New work cans the junction box usually remains with the fixed part and you just have the can dangling by the fixture wires. Old work cans have the box attached to the fixture itself so everything comes out the hole (obviously won't work with non-flexible wiring).

You are correct and this is old work. I was able to find an IBEW electrician and he indicated if it's an old work can with a hard box and cover attached then, yes, you can use that like any other light fixture to run additional conductors through.