Many already do it. You borrow a book recommended by a family member or friend. It might be useful to have a central and organized place for this.
Use existing platforms (like Facebook Groups) to create a closed private group. Invite your close friends and family members to join, and start recommending and lending books you read to each other. A special platform can also be built, with all the functionality to complement this activity (showing book details automatically, cheap shipping options etc.)