Creating a "sub-model" when Fine-Tuning

Hello Guys,
I’ve got a question: If you fine tune a model (e.g. davinci), the Open-AI documentation (OpenAI API) states that if you’ve fine-tuned a model, you can continue to fine-tune that model. My question is if this means that you add data to one existing model or if it creates a new model thats based on the older one with new additional training data.
I ask because I was wondering If you could e.g. create a “main-model” which knows how to write certain types of texts and then multiple “sub-models” which would be trained on user-specific data, so every user could get the text which is always similar, but with their own specific needs/preferences by getting their text generated by the “sub-model”

Thanks alot for every help!

Have a nice day!

I would advise looking into model distillation, although I am not sure it’s worth it. I think in-context learning is more advantageous than personalized distillation.