Can one be added at this stage and have the stone be supported properly?

If you have a footing as separate from the foundation, you should have a ledge for stone. To save money I guess the mason could use 4" block instead of stone up to within one course of finish grade.
There are cases where the foundation does not leave much or any of the footer exposed; it depends on how carefully laid out the footer trench was dug. It is an odd appearance to have the stone sticking that far out beyond the brick above, it can look fake/afterthought-ish.
Casey

Are you doing stone or thin stone? The thin stuff has a lot less weight and projects a lot less from the wall.

I would say it is too late to add thick stone to the foundation for the reasons Casey mentioned. An adhered thin stone or stucco scored to look like stone would be best but the joint at the brick will still seem odd and water might easily get behind it.

Where are you located? Will there be "freeze/thaw" issues? If the stone wall is more than just a veneer, an option would be to have the landscape stone "planter" be separate structure from the house, thus being free to move up/down etc. independently of the house. Just have expansion joint filler between the two to provide the break. Make sure the foundation for stone goes below the frost line though. Now if it's just a veneer and is only on the house, attaching to the house's foundation would be best. Now since either trade could perform this, back to your question who should end up doing this? Well the best or simplest down the road if there is any trouble would be the home contractor....why? Well if there is any warranty issue with water leakage, the home contractor could not place blame on landscaper for penetrating the foundation putting on the ledge; if he was the one who did the work. It's simplest to have one party responsible for things that are under a warranty, less legal problems down the road.

I'm curious as to how the home ended up so far in the air, when it could have been built to accommodate the mildly sloping lot. Looks like there's still room to build up the grading on the right side.

As noted above, a thin veneer would likely work best. No ledge needed. Followed by landscaping with its own foundation.

Probably finished (18 month old post) by now I would certainly hope...............

No, judging by the OPs other recent posts.

Then I will stand corrected worthy, I do not recall having seen anything.

My mistake. She's active but not posting re the house. It would be interesting to see how it turned out. Beth?

Be interesting to know why the foundation was so far above grade too!

Brick lug: (transitive verb) to laboriously pull a very heavy load of bricks.

Brick ledge: an extended part of a concrete foundation designed to carry the weight of brick masonry.

Grammar matters. She always has!

Although there is this Virgil

Yes, millworkman, thank you. It was my modest attempt at humor. I'll be quiet now.

yes, my bad I didn't mean to call you out on it.

I hate it when a brand new "Pro" dredges up an old discussion. Makes one wonder if they are just , um, what's that word? The word relates to canned "food". Darn. I'll think of it. ;)

Yes some sort of congealed meat product but the exact term escapes me at them moment as well..........