From my consulting work, I have seen the need to integrate a custom model into an LLM often since GPT-3.5 was released. I've started to call this type of model+integration an AI Plugin and I wrote a brief blog post describing the concept:

https://demajh.com/human_blog/ai_plugin.html

I would love feedback from anyone and everyone on the concept. I'm sure others have done similar work and any input you have would be much appreciated.