Amorphous transdisciplinary engineering is the application of back-end object-oriented provider services and front-end service-oriented micro- and macro-services. Macroservices define dynamic aggregates of large number of provider services (applications, tools, and utilities) with emergent multifidelity management. On the one hand, provider services are local/remote objects having independent limited functionalities that are dynamically bound to microservices. On the other hand, macroservices are request services in terms of microservices and other macroservices with metafidelities that specify required federations of provider services. Metafidelities are fidelities of fidelities. A metafidelity is used by a fidelity management system to select (morph) for a macroservice a collection of microservices at runtime. A macroservice request is called a mograms – model or program, or both. Service mograms created by the end users at the system of system level exhibit emergent behavior of service federations at runtime. A mogram's service federation with associated fidelity management is continuously morphing to the most effective collections of provider services while skipping unsatisfactory transient federations at runtime.