Sometime around the 1980s, I recall reading one of my father's 'mass market paperback' science fiction novels. The book was showing its age even then, so it's likely to have come from the 60s or 70s.

The basic idea of the story was that rich people had a ways of saving time not available to the 'great unwashed', and the saved time could be saved, in a 'bank'. When sufficient saved time was accumulated, the saver could have an extra day, which was conventionally taken between Saturday and Sunday. When the saver 'took' the day, it seemed to be in a world/universe/'phase-of-existance'/somethingorother which was just like the Real World, except that only the people 'taking the day' were there.

The story centered around someone who somehow managed to convince one of the rich people that he was one of them, for social reasons, and he learned about this time-banking scheme during the course of the story, and somehow made it public.