Patrick Stickles, the lead singer of the Brooklyn via New Jersey punk band Titus Andronicus, calls his new album — a 29-track, 93-minute, five-act rock opera about his manic depression called “The Most Lamentable Tragedy” (Merge) — “precious and belabored.” He means it lovingly, with a realistic amount of self-deprecation, long a key tenet of his songwriting.

It’s that inward-looking awareness, and Mr. Stickles’s caustic wit, which spares no one, that consistently keeps Titus Andronicus on the right side of pretentious grandeur. (Somehow even on “The Monitor” (2010), another concept album, in which he used Civil War imagery to address heartbreak and suburban angst.) On its fourth full-length album, out Tuesday, Titus Andronicus is doubling down on everything that has made it beautiful and absurd: multimovement songs, including a pair of nine-minute epics; thrashing shout-a-longs with unabashedly big guitar riffs; and therapist-couch honesty. Now there is also singing about time travel, covers of Daniel Johnston and the Pogues, a slopped-up rendition of “Auld Lang Syne,” at least one “Seinfeld” reference, strings (from the indie rock go-to Owen Pallett) and accompanying handwritten lyrics meant to guide the listener through every obsessed-over narrative turn.

None of which is to say this isn’t a punk album: On “I’m Going Insane (Finish Him),” Mr. Stickles just sneers the title line 24 times in two minutes, leaving time for a quick guitar solo.

On a recent afternoon, Mr. Stickles was Iggy Pop thin and motor-mouthed while seated on a ratty couch inside Shea Stadium, the Bushwick D.I.Y. space that serves as Titus Andronicus’s unofficial clubhouse. (The venue is also hosting the band for five sold-out shows leading up to the album’s release on Mr. Stickles’s 30th birthday.) He held forth with what could accurately be described as manic energy about the influence of his mental illness, why he prefers to spell everything out and the commercial ceiling for a rock band in 2015. These are excerpts from the conversation.