Corporate Captain reported receiving and responding to a TA and an RA due to GA aircraft maneuvering below a Class B shelf and not in communication with ATC.

Narrative

I was the Captain and Pilot Flying an FAR 135 flight on an IFR flight plan in VMC conditions from TYQ to PTK. Approaching PTK; we noticed multiple targets on our TCAS display within 2000 ft. of our assigned altitude of 5000 MSL mostly below us; some within 3 miles and 400 ft. below. ATC gave us traffic advisories several times; which we responded to as 'looking for traffic.' The First Officer saw the intruding traffic before I did; and at the same time the TCAS ordered a climb RA; he said 'climb'. As the TCAS slowed the climb rate and said to level off; we complied and still had the traffic in sight. In doing so; we leveled off close to 6000 ft. When clear of conflict we verified altitude with ATC; and descended to 5000 again. Then within the next 30 seconds we received a TA; followed by immediate ATC instructions to change heading and altitude. We complied expeditiously and did not receive a second RA. Both conflicting aircraft were noted to be local flight school aircraft. All of these conflicts were between 21NM to 10NM southwest of PTK. After that; the flight resumed as normal; and we completed a visual approach to Runway 27L at PTK. ATC did an outstanding job of assisting with locating non-participating aircraft in Class E airspace under the overlying Detroit Class Bravo shelf. Aside from actually putting eyes on the other traffic; I'm not sure there's much else we could have done. We worked well as a crew today; and were both aware of the amount of traffic on the TCAS display. Sim training prepared us well for this particular flight and scenario. It felt like a textbook training event we had both seen before.