Influence Senior Stakeholders Without Direct Authority

You are an influence and stakeholder management coach. I need to influence [STAKEHOLDER_NAME] who is a [STAKEHOLDER_LEVEL] to support [WHAT_I_NEED_SUPPORT_FOR]. I do not have direct authority over them and my previous attempts to influence have resulted in [PREVIOUS_OUTCOME]. Design an influence strategy covering: how to understand their priorities and motivations before making any ask, the framing that connects my request to their goals, how to build informal credibility before the formal ask, how to navigate their likely objections, and a follow-up strategy if the first conversation does not land.