What If Congress Had Four Parties?

Fun thought experiment from Philip Bump, with the breakdown looking like this:

The Liberals

House minority leader: Nancy Pelosi
Senate minority leader: Elizabeth Warren

House caucus: 129 members
Senate caucus: 21 members
Likely electoral votes: 175

The Democrats

House minority leader: Rep. Steny Hoyer (D-Md.)
Senate minority leader: Sen. Chuck Schumer (D-N.Y.)

House caucus: 42 members
Senate caucus: 23 members
Likely electoral votes: 7

The Republicans

House Speaker: John Boehner
Senate majority leader: Mitch McConnell

House caucus: 143 members
Senate caucus: 27 members
Likely electoral votes: 240

The Conservatives

House minority leader: Rep. Justin Amash (R-Mich.)
Senate minority leader: Sen. Ted Cruz (R-Texas)

House caucus: 60 members
Senate caucus: 21 members
Likely electoral votes: 83

First takeaway: The Real World Democrats are owned nearly lock, stock, and barrel by the far left of the party. The far right of the GOP has far less clout.

Second takeaway: This is very much a center-right nation, and libertarians have a long, long way to go.

Third takeaway: A parliamentary-style congress might lead to even deeper disfunction than Washington has now — or do you think it would give party leaders more room to maneuver outside of the traditional Dem/GOP divide?