I have a few ideas to expand the Senate for the MC.
Mingle: political discussions on the floor of the Senate, likely a very small Influence &/or Palace increase or decrease, very small possibility of an increase/decrease in Standing with one of the Houses, small (10s) expenditure of funds for amenities (social relaxations - coffee, drinks, mineral baths, etc)
Lobby: backing up your political discussions with lunches, drinks, bribes, etc, increases positive chances and rewards of Mingle, adds a minor (100s) expenditure of funds, while the MC selects topic (Liberty, Corruption, Control, etc) to Lobby, and if a Law gets passed on that topic the MC gets small Influence &/or Palace increase and an increase in Standing with the bill's owning House -- with a small chance of a decrease in Standing with a competing House.
Debate: engaging in official debate on the floor of the Senate in support of another House's bill, increases all the positive and negative chances, rewards and penalties to Influence, Palace & House Standing of Lobby, as well as double the expenditure of funds, also, if a law is passed on the MC's topic there is a small chance that the MC had a full amendment passed on the Law gaining the MC another very small Influence &/or Palace increase as well as Standing increase with the Bill's owning House, and, of course, a chance of a decrease in Standing with one of the competing Houses. This also includes a chance to be invited (MC & Wife/Consort) to dinner at the House that authored the bill. Additionally, who the MC brings to the dinner, and how she is attired, can result in another Influence increase or, if someone other than the Wife (or First Wife) is brought it would be a minor social scandal -- and an Influence penalty. Other social events and social connections could follow from these dinners.
Thanks for a great game!