I was thinking about I variant I want to try out tomorrow in a 6p TI4 game.
Each player would get a Public Objective Veto that they could use once per game. During step 2 of the Status Phase, in turn order when a Public Objective is revealed a Faction could discard the newly revealed public objective and draw a new one from the same deck in as the current Stage as long there will be 5 objectives of that stage in play after the Veto.
My idea behind this is to give players a bit of control over the objectives in the game. Since players are able to discard Secret objectives, why not some mechanism to discard Public Objectives as well? Do they Veto one now and be unable to Veto another objective later? Do they want to take away an easy tech objective if they are Sardakk Norr? What if there are not 6 planets with the same trait?