JAR-FCL 1.125 states:
"An applicant for a PPL shall complete at an FTO or an accepted registered facility the required instruction in accordance with the syllabus set out in...."
As the registered facility is required to maintain a training record, how can they do that accurately, when you train elsewhere? How will the instructor know what you did on the last exercise? How can they complete the course completion certificate if they have not completed all of the training?
Will a school actually agree to you continuing to train you when you are obbviously training elsewhere? I suspect not.
Whilst there is nothing to stop students changing schools, training at two consecutively, is not likely to serve any useful purpose.
Make up you mind where you want to train and get on with it!