Is the wall failing? You don't say what you're trying to accomplish .... protect the existing, or replace it? If the latter, you could drystack a wall IF your material was wide stones AND you put extreme batter (slope back) on the wall ... almost as if it was an extreme slope.

(You have explored/dug down at more than one section to check for footing?)

I have a dry stack retaining wall that is taller than that in an area with winter freezing and it has been solid for something over 25 years. But it is made of substantial rock that needed heavy equipment to move, and as Yardvaark mentioned, it has a good backslope to help keep it in place, as well as ties back into the slope. So having the horizontal space needed and constructing it correctly with appropriate materials and construction techniques are key.

It may be that you want to talk with someone who does just wall building as folks who do hardscaping may or may not have extensive experience with walls as opposed to flat work.

Wall is completely failing.
Trying to maintain a retaining wall given the huge tree roots there and the driveway next to it. This is the backside of the wall pictured below. Only checked one section for a footer. Demo today or tomorrow will check again.
Thanks!

If trees near houses, as above, are left with large limbs and foliage at ground level, instead of being a homeowner's "friend," become their constant, combative and often, unsightly enemy. It's going to be difficult/impossible to construct a replacement wall with all those limbs & branches in the way. Maybe it's time to turn this tree into a tree form ...? You'd probably want to reconfigure the path of the wall so as to give wide berth to the tree, as well.

You could do the drystack wall as I mentioned above (with pronounced batter) if the stones were 18"x18"x3", or larger, I did one like this as my first hardscape project as a young student ... for almost no cost. Went to the quarry and transported very heavy stones by CAR. (It was many trips but I had more time than money.) These days, I could rent a truck from Home Depot. You would not be able to do such a wall with small or lightweight stones. The only way it will be cheap is by providing your own labor.

yardvaark - beautiful, a few car trips to the quarry me thinks!

I have numerous dry-stacked stone walls, all of which are at least 5' tall and 100 yrs old. They used large stones starting deep in the ground and are two stone deep. Due to my neighbors' pneumatic machinery, tree digging and stupidity when replacing their wall that sits above mine with amodern-looking thing, a section of mine collapsed. Anyway, with a strong helper I was able to repair a 25+' section and it has held perfectly for 10 years. It's a joy to behold and adds beauty that will always complement your house. It's not beyond a DIYers skill if you study before beginning and be sure there is enough cant (batter). I'm not a particularly large female, so it's really more skill if there's someone to do the heavy lifting. Beautiful Yarrdvaark!!!! They exemplify the lasting beauty of this sort of wall. Around town many replacement wall use modern interlocking methods and they have fallen apart after just a few years, whereas the older stone walls stand proud. : ))

To echo points made by both NHBabs and Yardvaark it is certainly possible to be well over your required height with a natural stone wall. As NHBabs mentioned it might be better to search out a landscape contractor who specializes in wall work or natural stone. Backfilling behind the wall with an appropriate, free-draining gravel like CA-7 is important for the long-term stability. It's also important to have an appropriate compacted base below grade. Yardvaark also mentioned construction "(with pronounced batter)". That become a critical part of the process as you go higher and higher.

Both walls below are from Wisconsin "snapped drywall'. The first two photos are in the bottom of a detention pond and exhibit the batter previously referenced. This wall has been in place for seventeen years if memory serves. It's about 6' tall at its highest point. As a point of information we bridged the concrete channel in photo #2 with 3/8" plate steel.

The second wall in front of the home has been in place for over twenty years and is not quite 4' tall at its highest point.

Both walls are stable and aging nicely. Based on the vintage of your home any natural stone wall construction would be more in keeping with the style than a more modern, modular wall. Best of luck with your project.