“I take the lead, but I have to have her approval,” Mr. Levinas said. “Usually I get it.”

Their trove, primarily paintings and sculptures, seems to oscillate between two poles: spare conceptual pieces and works of lush color. Mr. Levinas recently chatted about his taste in art and how it has evolved. These are edited excerpts from the conversation.

Since I am turning the tables on you, what do you normally start with when interviewing a collector?

I ask them the motivation for them to start collecting. And then why they decided to share the collection with the world.

So, what’s your answer?

Because I love it. I love to help artists, but I also enjoy living with the pieces. Take this piece by Jose Dávila [“Untitled,” a stack of bricks surrounded by neon]. I saw it in Mexico. He’s big now, but he wasn’t big when I bought this piece. The point is that when I saw it, I said, “This is so beautiful to me.” It doesn’t mean that it’s going to be beautiful to you, but it touches me and it talks to me.