It’s been five years since Bryan Cranston’s Tony-winning turn as Lyndon B. Johnson in Robert Schenkkan’s “All the Way.” Now Schenkkan has followed that epic historical pageant with a sequel, “The Great Society,” opening Tuesday at Lincoln Center’s Vivian Beaumont Theatre, that like LBJ’s second term dwells mostly in the shadows of its predecessor.

This time, LBJ is played by “Succession” star Brian Cox, a veteran character actor with even less of a physical resemblance than Cranston had to the hulkingly tall, broad-shouldered, doughy-faced Texan who became the nation’s 36th president after the 1963 assassination of John F. Kennedy. While he maintains a commanding presence on stage, buttonholing opponents and blindsiding them to follow his agenda, Cox’s accent sometimes wanders and he never quite summons the imposing menace of the real Johnson.

Perhaps, though, that reflects this period in Johnson’s career, when the veteran wheeler-dealer found himself nearly overwhelmed by crises both domestic and foreign: the continued challenge of civil rights at home, with activists like Martin Luther King Jr. (Grantham Coleman) pushing for even speedier reform against the resistance of Southern Democrats like Albama Gov. George Wallace (David Garrison), and the escalating military operations in Vietnam led by Defense Secretary Robert McNamara (Matthew Rauch).

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As he did in “All the Way,” Schenkkan packs a lot of plot into his nearly three-hour drama — with most of the 17-member cast playing multiple roles. The result is never confusing, thanks in no small part to Bill Rauch’s direction, but it can leave you longing for more context and characterization even as you observe the parallels to our current political fractiousness.

Rival-from-the-left Robert F. Kennedy (Bryce Pinkham) and FBI boss J. Edgar Hoover (Gordon Clapp) are reduced to mere walk-on roles, while Vice President Hubert Humphrey (Richard Thomas) emerges as more of a sounding board and punching bag than a rounded political player. And the handful of female characters, including Lady Bird (Barbara Garrick) and Coretta Scott King (Nikkole Salter) are barely seen at all, let alone heard.

While Schenkkan admirably compresses a lot of story into a relatively fast-paced narrative, one wishes he’d taken more cues from Shakespeare’s history plays, pausing occasionally from his fixation on the political process to convey a fuller sense of the major players. Cox’s Johnson delivers a few folksy stories that are meant to stand as parables for the events unfolding around him, but they don’t go far enough to understand the why behind the flurry of events. Is it too much to ask for a soliloquy or two?

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Johnson is indeed a Shakespearean figure, a Southerner who stumbled into the White House by a tragic accident of history but who defied his Southern upbringing by embracing JFK’s civil rights agenda at the risk of alienating his own base — and who used his natural political skills to vanquish (or at least co-opt) his rivals.

But we never come to understand why he allowed Vietnam to spiral out of control, or even the real reason he decided not to seek re-election in 1968 for his own second term. The LBJ that emerges in “The Great Society” is less a portrait of the man, and more of a sketch.