Situation
House Harkonnen has moved on House Atreides and the party is at the Landsraad council of Houses trying to get sanctions against House Harkonnen.
Take 5e.
Could be handled free form, the party interacts with NPCs and makes their proposals and the DM roleplays the NPCs and adjudicates results. Could be in-depth, could be light, could be first person roleplaying or second person approaches, could focus on one character or the party as a whole or multiple characters sequentially.
Could be handled using the standard 5e skill system with the DM deciding to call for a roll against a DC to determine success, persuasion to get what they want, the party describes their approach or roleplays stuff out and then a die roll is used engaging the mechanics for a skill check, character stats, possible advantage and disadvantage, bardic inspiration, etc. This engages some of the character aspects, build choices, possibly approaches taken for advantage and disadvantage, and includes an element of chance and uncertainty in the result and is based on roughly how difficult the DM assesses the challenge of the task.
Additional rules could be a 4e style skill challenge, multiple characters doing different things to accumulate progress towards the desired end result. Multiple characters involved and engaged sequentially, multiple approaches, not a binary yes no on a single die result but multiple checks with impacts so there can be successes and setbacks and complications, possibly over multiple rounds of party actions, different aspects of the situation can come in, approaches impact difficulty and there is an element of chance involved at multiple stages.