I think you are a bit confused about the use of MTFs. Class-D riots will most likely be handled by on-site disciplinary / security staff, and any escaped anomalies will be handled by more specialized MTFs on a case to case basis. Off the top of my head, the most "multi-use" MTF is 16 Tons, which is made of the members of GoIs who will of course have different skills depending on their GoI of origin.
If a Euclid class anomaly escapes that is spectral or undead, they might send in The Silencers. If it's a reality bender, they'll likely send Achilles' Heel. If they have no idea what it is yet, they might send D-Class after it at first, or a reconnaissance mission, but there has never been an MTF that didn't specialize in something. "Multi-use" is basically setting them up for failure because every anomaly has specifications and they can not be specialized in everything.
As for exploring anomalous locations, we have an MTF or two that do that. Angle Grinders deal with areas that have anomalous topology or geography, and Home Improvement deal with creepy anomalous buildings (investigation and demolition). The point here being that there's not gonna be an MTF that is as multi-purpose as you are hoping, but there are already existing MTFs that you can use if your series is going to kick off with the investigation of an anomalous building. I would suggest using one of those established instead of making your own, unless you have a very specific role for them to fill.
Say, an MTF that is specifically made up of Foundation Historians and agents whose lives have been anomalously prolonged, who are then to investigate holes in Foundation records. Sort of an "internal surveillance" team, which would be perfect for investigating a Foundation site that popped off the map.
Also, because it's been bugging me, you mean "edition" every time you say "addition".
And lastly, I would say this is a solid start for a series. If you want a long, weaving mystery, starting with investigating an abandoned SCP Site would certainly do it, and following an MTF's adventures would be a fun series. I just think there are some problems with your set up (and also there's not much here to go off of, if I were to nitpick).
