I would like to sepeculate, that it doesn't make any sense, firstly as instruction needs to be done via a registered ATO (Flight School, Aero Club etc...).
Of course a single instructor could go and open a flight school i.e. register his/her ATO at the authority, however this involves all legal obligations and requirements plus insurance.
Secondly I doubt it would be viable or feasible to abuse your own private aircraft for this purpose - because you need the ATO in any case so you might as well run the airplane under the ATO and not privately or offer an existing ATO to utilize it for training.
Last but not least, I doubt it would be feasible to make a living, not even to mention to finance your own aeroplane.
Why take such a risk ?