For big important political social encounters, I find Opposition Research and using Inspiration/Action Points for flashbacks to be super useful.
The smart guy characters can have actually looked into the area and relevant situations and practices. The strong guys can have turned out to have gone out to the pubs with the guy's bodyguards the previous nights and overheard choice bits of his current situations. The sneaky ones can have broken into their office and gotten a look at their papers. Then all of those help change the DC or roll in the present, making it so even if not everyone is speaking in the moment, they all got to contribute.