There is a need for information, application, and other enterprise architectures which are robust and flexible enough to meet the challenges of today’s heterogeneous, rapidly changing, digitally networked environment. Developing advanced architectures may prove essential for achieving emerging research, business, and social goals. Indeed, the profoundly changed landscape suggests that a new paradigm may be needed, an inter-enterprise architectonic (I-EA) informing architectures capable of integrating all key components and processes in an increasingly interconnected environment. To meet this challenge, a systems architectonic is outlined that is based on the trichotomic category theory of Charles S. Peirce. Trikonic Inter-Enterprise Architectonic involves a pragmatic approach to the observation and manipulation of diagrams as models of enterprise and inter-enterprise processes.