I'm looking at a re-imagined Princes Risborough using the assumption that the Midland had actually managed to get the London, Buckinghamshire and East Gloucestershire railway built which could have turned the Princes Risborough to Thame into a joint route, Thame becoming a junction. The southern end where the line from Amersham would enter Princes Risborough would probably need to be amended but I'm not sure northen end heading for Thame would need any alteration of the track plan. (I'm looking at 1913 for the setting)
As far as I can tell this would allow me to run GWR, GCR, Midland and L,B & E.G. stock into the re-imagined Princes Risborough.