THE DEMOCRATIC PARTY’S DOMINANCE in the Massachusetts Legislature is a matter beyond dispute. Since 1978, when a constitutional amendment reduced the number of seats in the House of Representatives from 240 to 160, the Democrats’ veto-proof two-thirds majority in that body has never dipped below 123 (17 votes more than necessary for a veto override). During those same 41 years, Democrats have held a veto-proof majority in the Senate for all but two.

The bad news for Republicans in these numbers does not necessarily mean good news for Democrats. A recent report by MassINC on some worrying disparities in civic engagement among the state’s residents concludes that the Democrats’ supremacy, paradoxically, has left the party weaker rather than stronger. Democrats hold more legislative seats than their voter registration numbers warrant, yet most of those Democratic legislators have little power to influence legislation, particularly in the House, where the Speaker and his leadership team largely set the agenda.

Certainly on policy matters House leadership is the tail wagging the Democratic Party dog. Advocates looking to advance the Democratic Party platform have in recent years found the House to be a much less hospitable place than the Senate, which has delivered some platform priorities that House leadership has rejected (safeguards for immigrants, ambitious climate change legislation), and has delivered others in a timelier way (criminal justice reform, protections for public employee unions).

The speaker seems content to keep the Democratic Party platform at arm’s length in the House, recasting this divide as a pleasing example of the party’s inclusivity. “I think fortunately we’ve been a party of people of many different views. And that’s important,” he said in 2017. “We’re an inclusive party of people of all views, so I think that’s a good place to be and that’s why I’m proud to be a Democrat.”

Enacting the Democratic platform, in other words, is less important than electing more Democratic members to the House.

And the speaker has a big political action committee busy at work electing Democrats. Operating under the name “Committee for a Democratic House,” it rivals the Democratic State Committee in resources. And unlike the State Committee (and unlike the considerably less affluent Committee for a Democratic Senate and the two PACs operated by the Republican Party), the speaker’s PAC involves itself in primary elections, providing support for Democratic House incumbents facing primary challengers.

The Committee for a Democratic House began helping incumbent Democratic House members facing primary challengers in 2016, giving six of them cash donations of $500 (the statutory maximum. Four of the incumbents won their primaries and went on to win re-election, while two were defeated.

In 2018, the PAC assisted 11 incumbent House members in the primary election, most notably Colleen Garry of Dracut, who is widely regarded as one of the most conservative members of the House, let alone the Democratic Party, and who, in the weeks before the primary election had voted against two of the Democratic platform priorities that the speaker had brought up for House votes — bills dealing with reproductive rights and gun control. Nine of the incumbents, including Garry, won their primaries that year and two lost.

For political parties, a primary election serves as a useful competition that invigorates and expands the party base, hence the Massachusetts Democratic Party’s prohibition against favoritism at that stage, including the bar on expending financial resources in contested primaries. For the speaker’s Democratic House, however, contested primary elections threaten to eliminate the advantage that incumbency holds in general elections, a threat that may in turn imperil the supermajority.

Looking forward to 2020, 10 House Democratic incumbents have challengers to date. Also facing a challenge, it seems, is the state Democratic Party itself. Will the party continue to allow the speaker’s PAC to intervene on behalf of incumbents in primary elections, when those elections help to energize the party and when the number of primary candidates is now on the upswing, having grown since the all-time low in 2012?

The party has a tool at its disposal that so far it has declined to use. A state statute gives political parties the right to control the use of their names by other organizations. And under Democratic Party bylaws, permission to use the word “Democratic” is to be withheld from any organization that endorses candidates in a contested primary. So it would seem that the Democratic Party could sue to require the Committee for a Democratic House either to stop endorsing primary candidates or stop using the word “Democratic” in its name.

A lot for Democratic Party officials to consider, including the financial support the speaker’s PAC has contributed and could continue to contribute to party.

How does “Committee for the Speaker’s House” sound?

Margaret Monsell, a former assistant attorney general and former general counsel to the state Senate Committee on Ways and Means, is an attorney practicing in the Boston area. She is an unenrolled voter.