Pilewort, Burnweed, remove now to keep from seeding. Erechtites hieracifolia. Here is a link that might be useful:

Thanks. Looks about right so far. Any recommendations for treatment? Also, now that I'm seeing pictures of this menace I realize that I also had a much larger version (essentially a tree) with a base trunk diameter of almost 5 feet across! The tree itself was about 30 feet tall. Is it possible, er likely, that this single root system is responsible for smaller stalks popping up 40-50 feet away???

Symphytum species i.e. a Comfrey. Possibly S ibericum or S grandiflorum but those are just suggestions.

Without knowing what the other grasses are, it makes the decision for us...we cannot use selective herbicides for it. Hopefully you have patches of it and not wide distribution. If so, hit those patches with 2-3 apps of round up (glyphosate). They'll wither away and then you can overseed bare areas. This, again, makes it tough because we don't know what other grasses you need to overseed with. I would recommend spraying before digging in case it is reproducing via stolons...kill it all. Glyphosate will kill whatever grasses it hits. To combat this, I have a set of all different diameter PVC pipe couplings. Actually, I'm preferring the reducers lately, like this: http://www.lowes.com/pd/Charlotte-Pipe-2-in-x-3-in-dia-PVC-Adapter-Coupling-Fitting/3132737 I select the diameter for the size of the grass I want to spray and place it over the top and spray inside the coupling thus saving the grass around it so you only have small bare spots. Now, if you have warm season grasses, those spots might fill right in, but that won't be the case with cool season...you'll need to overseed. Oh, this is important. That stuff, even if we are wrong, has seeded your yard. You'll want to look into pre-emergents like Prodiamine and Dithiopyr. These stay active in the top layer of soil to kill seeds that try to germinate...they do not kill your established grass. Keep in mind, that if you are overseeding, it will kill that too. You have to apply these later...I know Prodiamine is 60 days after seeding. Also, Prodiamine can last 8-9 months in the soil, where Dithiopyr is shorter and can last 3-4 months....depending on rainfall. In short: If you have cool season grass, kill what you need to now. Do your overseed project around the beginning of Sept, and put down Prodiamine around the beginning of Nov. If you have warm season, somebody else will need to comment, but I believe you seed that in the Spring, not fall. I would kill what you need to now and put down Prodiamine 2X between now and again in Nov....re-seed in April...if you even need to. Lastly, if you feel yourself becoming a lawn nut, consider a full renovation so you know exactly what grasses you have and can react accordingly (and with less effort) in the future. Cheers.