newlife99,
Is this your own house?
You said that, for the most part, you are not undermining the existing wall, that the wall has not settled, that there are no cracks, and that you are not adding any new load to the wall. I'm assuming that the clay is relatively stiff or hard.
What is the condition of the existing basement room on the opposite side of the wall? Could you underpin this wall from the existing basement side if you had to?
I know this is not what others here would say but, if this is your house, if you can work from the opposite side of the wall, you may want to not underpin the wall at this time. Consider building the addition and then monitoring the wall for settlement for a while (maybe a year or until you get settlement and cracks). Then, if you do have settlements, you could then underpin the wall from inside the old basement. This may be a bit more expensive and disruptive than underpinning now from outside the existing basement but it can be done.
Remember, you have had no settlements to date and you are not undermining the existing wall with your addition. You can spend some money underpinning now or you can spend a little more money underpinning and patching possible cracks later IF YOU NEED TO, and maybe you won't need to. It's your house and your gamble.
Remember though that whether or not you underpin now, when you work along side of the existing wall, do not let the ground along the wall get wet, muddy, and soft or you will settle the wall. Don't let water build up along the wall. Make sure that roof drains and downspouts are directed away from the work area. And, get the new, adjacent, wall footing built and backfilled ASAP. If you want to be a bit more conservative, build the new wall footing incrementally in several short sections so that you haven't excavated along the entire wall at one time.
If this isn't you own house, forget what I just said and get ready to underpin. If I had to underpin the wall, I would use unreinforced concrete underpinning piers. I would install the underpinning in sections, each pier about 3 to 4 feet wide. I would make the bottom of the underpinning about 6 inches to a foot deeper than the bottom of the proposed footing. I would pour the underpinning concrete to within 2.5 or 3 inches of the bottom of the existing wall and then drypack the remaining space the next morning after a pier is poured. No two underpinning piers within about 8 feet edge to edge of each other should be excavated or unpoured concurrently.
With any underpinning operation, you can expect to see some settlement. You may not get any but you should expect to see about 1/4 inch. It is not unusual.