How about the moderate party being a democratically governed one, where it's members have an app that identifies them so they can only get one vote. Then whenever the candidate they choose votes on issues, the people decide via the app, how that senator will vote.

If he doesn't go w/ the people he is banned from the party. in this way the moderate party would cater to the demographic of the area... where one member might vote for gay marriage in NY, another in Alabama would not, but still be part of the same party, but only answer to their local constituents.