You should note that the operator's conversion course (OCC) requirements are applicable to NCC as well as AOC flying. This is probably because mistakes are made when either pilot misunderstands what the other has said or does or is not familiar with the company procedures, equipment and processes. This means that you can not hop around aircraft flying freelance on private operations without completing the operators conversion course. The regulations contain the words ' when changing operators' in the requirement to conduct an OCC so if you change operators one day and then back the next then by inference you are required to complete the OCC each time. The basic information applicable to all flying, including private operations, can be found in ORO.FC.100 onwards and the additional requirements for AOC flying in ORO,FC.200 onwards.
If an operator follows the rules it is technically possible to fly for different operations but it is very time consuming and expensive to the point of not being worth the time and trouble and the risks of a non-compliance are high. This applies to private (NCC) and commercial (AOC) operations.
Contrary to what has been written above, it is your problem as you are personally responsible for your actions or omissions.