According to the Project Management Professional (PMP) guidelines, when a project faces significant resistance from a senior-level executive, the project manager should work with the project sponsor to determine an appropriate response. The project sponsor typically has the authority and influence within the organization to address such issues. This approach aligns with the guidance provided in the Professional in Business Analysis Reference Materials, which also emphasizes the importance of stakeholder engagement and the need to address stakeholder concerns in a timely and effective manner. References: Project Management Professional (PMP) Certification, PMBOK Guide, Professional in Business Analysis Reference Materials.
Please refer to the respective guides for more detailed information.