I’ve roleplayed in a play by forum campaign of linked Doctor Who adventures. We played using Call of Cthulhu RPG rules, and the games were suitably horror themed. The Time Lord (not the Doctor) and companions faced enemies in 1930s British Museum, far future Pluto, 1970s Dunwich in Suffolk, Ancient Rome around the time of Julius Caesar, and wartime blitz hit London. I had to drop out after that because my neuro disease meant I couldn’t keep up with the games, constantly forgetting stuff. It didn’t help that as forum games they were very prolonged, and my memory was really shot! But great fun. Someone else is continuing to play my character - a young Scottish history schoolteacher from the 1950s, one of the companions - in continuing adventures in 16th century France. The Time Lord also recently regenerated.