- You may be looking for the Virgin Decalog short story or the Faction Paradox short story.
A timeshare was a property that existed in several different time periods, "all at the same time".
Holiday Opportunity Promotions operated timeshares, but eventually the Time Lords closed all but one. The member of a vampire-like race bequeathed the first week in November of that timeshare to the Doctor. His sixth incarnation and Peri visited it in 1929, unintentionally causing various time zones to overlap. A Time Lord was sent to correct the problem. (PROSE: Timeshare)