Is it really LLMs (plural) when you only have OpenAPI integration?
See for example Anyscale Endpoints https://app.endpoints.anyscale.com/landing and https://github.com/AmineDiro/cria
You could have more flexibility by abstracting out the underlying LLM APIs, but then you also have a bigger deal with supported features of different APIs, the same conceptual feature supported with very different parameter structures, etc., etc.