Standard C of A
The 'Private' catergory C of A has gone. Some aircraft with the old private cat will be due for their 'star' this year and that will be the end of it.
Therefore the rules with regard to private catergory will be defunct. The CAA exemption for sole owners will therefore have no effect. But that won't matter.
To use the Standard Catergory aircraft for flight instruction then the last inspection of the aeroplane must have been completed by a Licensed Engineer and a Certificate of Release to Service issued. All other aspects of the aeroplane must be able to comply, such as an in-life engine (not exceeding the 20% extention).
Flying Instruction is not the public transport of passengers and therefore a Public Transport Certificate is no longer required under EASA. I cannot see therefore why a part owner cannot learn to fly on their group owned aircraft unless the condition of the aeroplane does not comply.
The rules with regard to ab-initio training only at a FTO or RTF of course applies.