Organizational ambidexterity balances exploitative and exploratory behaviors so that organizations are able to exploit their existing competencies while simultaneously exploring new opportunities. Similarly, ambidextrous cybersecurity (AMBI-CYBER) focuses on the protection of data, systems, and networks, while fostering the rapid introduction of new technologies within a company. This balance is linked to cybersecurity absorptive capacity and defines the "Cybersecurity Efficient Frontier." In this paper, we view AMBI-CYBER as a combination of organizational as well as technological and cultural competences which rely upon a multifaceted, multimodal, multinodal, and multilevel set of skills and capabilities. We outline the anatomy of the AMBI-CYBER architecture adopting a balanced scorecard, multistage approach under a 7Ps stage gate model (Patient, Persistent, Persevering, Proactive, Predictive, Preventive, and Preemptive). Such an approach emphasizes the need to enable a complex, nonlinear, adaptive process of dynamic intangible organizational assets, resources, and capabilities across a performance frontier where we aim to optimize safety, security, and privacy effectiveness and efficiency. We also suggests that the Quadruple/Quintuple Helix Innovation model may promote AMBI-CYBER enabling a locus-centric and triple-bottom-line-centric entrepreneurial process of discovery followed by development, exploration, exploitation, and deployment.