When I did my PPL back in the dark ages (OK, 1970s), I had many different instructors - it just depended who was free as I wanted to do it as quickly as possible and couldn't afford to wait for a favorite guy to have a free slot (I am a firm believer that doing it quickly - about 7 months in my case - prevents that 'two steps forward one and half steps back' that happens when gaps between lessons are long).
I think it was an excellent system as one could discount the odd 'not on my page' guy's methods while still learning from him. It taught me two valuable truths about flying:
1) There is often more than one way to do things.
2) You have to be self-reliant.
The latter point refers to the need, when having a mix of instructors, to manage one's own progress through the syllabus and not rely on being spoon fed and led by the hand. It was not uncommon for an instructor to jump into the RH seat with a "right, where are you up to? What do you need to do today?".
Of course the CFI would be keeping a '35,000 foot view' of one's progress and would be one of the regulars one flew with, and all lessons were documented to ensure the syllabus was covered with no gaps.
Worked very well for me. Solo in 10.5 hours, PPL in a tad over the minimum (both of which I put down to some previous gliding experience, but mostly to taking lessons with minimum gaps between).