Although there are different theories about the adoption and implementation of technological innovation by companies, they have an organization/individual-centered approach. The aim of this study is to propose the Technology–Organization–External–Sustainability (TOES) framework, a technology adoption theory, an extension of the Technology-Organization-(business) Environment (TOE) framework, to assist companies in adopting and implementing technology through a holistic approach. Design Science Research was used to structure the TOES framework and the Delphi method for its evaluation and improvement. To examine the potential of the TOES framework, 40 maturity and readiness models found in the literature were examined, which were created to assist in Industry 4.0 implementation projects, according to their common element of analysis—their dimensions. An important finding was that the TOES framework allowed us to identify that most of these models focused predominantly on technology; therefore, they do not always allow for a general analysis of the company, nor do they consider the external competitive scenario or sustainability as relevant contexts for analysis. The theoretical and practical contribution lies in the presentation of the TOES framework that incorporates sustainability as a relevant context for analysis, expanding the theory of the adoption of technological innovation. Another theoretical contribution is to alert researchers that maturity and readiness models for Industry 4.0 implementation projects should take a more holistic approach. It is suggested to use the TOES framework in other areas of knowledge, such as medicine, engineering, technology, and science, among others, to test its potential.