OP

Your organisation has plans that spawn several decades, sometimes centuries. What is the mechanism the ensures all members of the organisation work together and objectives do not change under new 'management'?

You all play the game of power. You play it at a level far above any of us but the same rules still apply. You are incentivised to maximise your own power (or that of your sub-organisation, house), while at the same time ensuring that your peers do not erode your own power to add to theirs. Playing at what we all understand to be the highest level would naturally generate pressure on any equilibrium of power that exists at your 'level'. Eventually some are going to want more, rivals are going to appear weak, etc.

How could the organisation you are part of have survived for so long without it devolving into infighting and power struggles? If it is based on a cartel like agreement you have, how would the addition of new members be managed? That management would still be at the discretion of whoever was 'in charge', you yourself said you have the power to override people so this must exist.

The only solution I can see is that there is a level above you, who you all report to, which can resist the decay of time and stay consistent throughout the ages to ensure the 'plan' is carried out. Does such a level exist?