Charter, also called air taxi or ad-hoc flights require certification from the associated country's regulating body such as the FAA in the U.S. The regulations are differentiated from typical commercial/passenger service by offering a non-scheduled service. In the U.S. these flights are regulated under FAA Part 135. There are some cases where a charter operator can sell scheduled flights, but only in limited quantities.
Though the early Lockheed Jetstar had four, most production business jets have two jet engines, mostly rear-mounted podded engine. If mounted below their low wing, it wouldn't allow sufficient engine clearance without a too long landing gear. The HondaJet is the exception with its over the wing engine pods. Dassault Falcon still builds three-engine models derived from the Falcon 50, and the very light jet market has seen several single-engine design concepts and the introduction of the Cirrus Vision SF50 in 2016.