Niche publishers like The Folio Society have been re-purposing publishing content into finely re-worked books for many years. These titles have expressly designed covers, often come slip cased and contain commissioned illustrations that were never in the original versions. They are beautiful objects but they are also one person's representation of design and manufacturing and other than the high quality there is only minimal uniformity across the titles. On a different level other titles from series such as Everyman's Library are similar in format but not of the unique quality as The Folio titles.
With not too much work you could create your own collection of titles. It would be one of my goals to work with my own editor and book designer to select titles, design a look for the exterior and interiors of the books and start publishing my own Modern Classic collection. With the costs of publishing one title through sites like blurb and Lulu.com it isn't an idea that is too far fetched. In the short term the content would likely be limited to public domain works but I believe over time more publishers will allow 'be-spoke' versions of their content where the consumer pays for the right to 'publish' the material for private use.
For someone like me who values the book as an object, creating my own title list of classic books with covers and interiors designed by me could become a viable avocation and source of deeper engagement in reading.