Acclaimed songwriter Ezra Furman began her band life back in 2006, as a Tufts University undergraduate. Now she’s back at her old stomping ground, or at least near it.

This Tuesday she continues a monthly residency at the Rockwell on Davis Square. Billed as “Ms. Ezra Furman Doing What She Wants,” it’s a solo show with no formal setlist. “I’ll still play my hits, assuming I have any,” Furman said this week. “I can do new songs, I can do cover songs, or I can just stand there and beat a drum. But I really want people to get what they paid to see, which is an impossible task, especially for me. If I have a signature song I’d have no idea which it is.”

The Rockwell shows will be solo and stripped down. But on disc, especially the current “All of Us Flames,” Furman can conjure dramatic electronic soundscapes, making the songs as intense musically as they are lyrically.

“I’m always trying to crack the code of how to make the greatest record ever made. And I know that’s too high an ambition, almost unproductive. But how can I deeply move someone? Everything has to be in service of that — ‘Can I beat that thing I did two and a half years ago? Maybe the last one cut deep, but this one has to cut deeper.’ I don’t really have a loyalty to any particular sounds but I do have a loyalty to truth and spirit.”

One of the new songs pays tribute to a childhood idol, it’s called “Ally Sheedy in the Breakfast Club.” But no, as far as Furman knows Sheedy hasn’t heard it. “I’d love to know if she has — but then, maybe I wouldn’t. Something about that character she played proved deeply useful to me. But I’m afraid she’ll hear it and say, ‘Oh God, another psycho’.”

Her best-known work may be the soundtrack she did for the Netflix series “Sex Education,” but that’s a gig she has mixed feelings about. “Along with the soul searching spiritual project that is my artwork, I have this craft that I know how to use — like, I can write a song for somebody who needs one. ‘Sex Education’ was the first thing I ever did that wasn’t completely about me. It was like my corporate gig, my Starbucks job.”

One personal change happened in 2019 when she went public as both a transgender woman and a mother. This brought a wide range of reaction, largely but not entirely supportive. And though the album had already been written, some of the urgency turned up on the tracks.

“The point of that little moment was, have you even seen a trans woman be a mom? I haven’t, and I wanted to show myself doing it. I had felt it made more sense to guard my personal life, because of the way they treat me on the internet. I hadn’t realized the story was going to become such clickbait. But I felt a deep lack for trans people, that we didn’t see a model for us becoming parents. The less we can see of that, the less we can imagine of our own futures.”

Still, the album’s theme of fighting for love in a hostile society is hard to miss. “Well, I’ve felt like it was me against the world long before now. I just had a punk mentality, the first music I loved was punk rock. And to me that’s not a sound you have to be loyal to, I just think of punk as a strand of postmodern thought. It’s philosophy that had a beat.”