Imagine, as a start, that somewhere from six to nine senators agreed to work together, either as a formally separate party or through an agreement of factions in either party. The moderate bloc would enter into a coalition with whichever party’s leaders offered it the best deal to change the rules under which the body operates. Today, the majority party makes sure that Senate floor time is consumed with proposals that unite its coalition. Various bills with bipartisan groups of co-sponsors get written all the time, but this kind of legislation gets a hearing only when it serves the majority leader’s designs.

A moderate bloc could demand rules that prioritize bipartisan bills. The lack of space for this kind of legislation is a primary complaint of a huge share of senators, including fairly ideological ones. But the bulk of members prioritize partisan solidarity over dreams of a more open Senate.

The standard solution to party leadership’s monopoly control of the agenda is freer use of “discharge petitions,” which allow members to force bills out of committee and onto the floor of Congress. One risk of that approach is that Congress could become very difficult to manage. But in a Congress in which moderates held the pivot of control, discharge petitions would not be necessary. The agenda would still be set by leaders, but (unless their majority was very large) in consultation with the moderate bloc. The majority party would have strong incentives to support at least a vote on the bills supported by the moderate bloc, because its control of Congress would depend on keeping the moderates in the fold. And if a concerted bloc of moderates forced a more open process onto party leaders, many members would be quietly happy.