The answer is yes! However, this is only possible if the model with whom you have your show has enabled the recording option. Not all models choose to do this, but you will know it beforehand; if when clicking on “Start Private” you see the message “You can save this show”, then it’s your lucky day!
As soon as the Private or Cam2Cam is finalized, you will be asked whether you want to save that show recording to your My Collection. Hit “Save”, and it will slip in your video gallery so that you can access it and re-watch it anytime.
For Private shows the model will have access to a copy for herself. However, in the case of Cam2Cam, only you will be able to record and save this show. Note that only the model’s stream will be included in the Cam2Cam show recording.