If you decide to upgrade to private room, the conditions depend on the timing of your decision, pending of course on the availability.

Before the trip: Possible by paying the price difference at the time of your decision (e.g. if you bought an early bird ticket but decided to upgrade during normal prices, you pay the difference at normal prices).

After the trip has started: If you decide to upgrade during check-in, if there is room available, you will have to pay the price difference plus 20% of your original payment as penalty.