What do we owe each other? How far should a person go, how much should a person sacrifice to ensure their fellows are cared for? What exactly are the obligations we have to one another? These are some of the questions raised by Charles Baxter’s engaging new collection “There’s Something I Want You to Do.”

The title makes the theme explicit, but it also appears in some form or another, usually as a line of dialogue, in every story, one character asking another for help. The request may be for something as inconsequential as an email, or as difficult as taking in a former lover who is now homeless. But each time, the line signals the reader: here is the story; the moral history spinning off from this moment is what the story is about. It’s an ingenious trope and gives the collection a thematic continuity.

Baxter doesn’t leave it there. He further builds his notion of our connectedness by employing an ensemble cast of characters. Several reappear throughout the collection. We see them from many angles, the protagonist in one story, a supporting role in another.

The cycle consists of ten stories split into two sections: Virtues and Vices. The titles of the individual pieces conform to their section headings: Charity, Loyalty, Chastity, Charity, Forbearance; and Lust, Sloth, Avarice, Gluttony, Vanity. Don’t assume they are morality tales, with simple premises and equally pat resolutions. Baxter is far too subtle a writer. These are stories of people behaving as people, not types.

Though all are very good (“Bravery” and “Charity” both appeared in the “Best American Short Stories” series), some of the most affecting tales come in the second half. “Vanity,” for example, unfolds with breathtaking economy. Nine pages, a conversation between two passengers during a bumpy airplane ride, and at the end, Baxter delivers a short, sharp shock that sums up the whole of humanity’s religious philosophies.

“Gluttony,” shows us pediatrician Elijah Jones. He’s overweight, a compulsive eater (perhaps brought on by stress from caring for seriously ill children), constantly stuffing himself with potato chips and beef jerky on the daily drive home from the hospital. However, his true gluttony is for his family. It seems he can’t love them enough — their strengths and foibles, their worries and hopes — he gobbles them as sustenance for his soul. And why does he do this? As a holding tactic against death, against the inevitable that his profession and personal experience has demonstrated will eventually claim us all.

Death is the other actor in these stories. While each tale might individually touch on a facet of the human personality, coloring the background is Death’s dark subtext. Time is running out, Baxter seems to be saying. Always act with wisdom, grace and generosity. If you think, you might get a second chance to do better, to show more compassion and understanding the next time you are called upon, Death is there to admonish us: Don’t kid yourself.