Is it possible to share and merge classification models?

I’m starting my machine learning study and I’m trying to figure out a simple question:

Let’s say that I have two models, one that recognizes cats, and another one that recognize dogs.

Now I have a camera and I want to recognize both cats and dogs using my models.

Obviously, I don’t want to create a third model to recognize both, having all the work to label each animal, so, is there a method to “merge” both models into one?

I’m asking this question because I want to understand one thing: why ML engineers don’t share their models so then we can create aggregated models? For example, if a person A has a model that classifies people and a person B has a model for animals. Why they can’t just share their models so then each one will have a more powerful model without needing to re-train everything?

I’m sorry if this is a too basic question, but I didn’t see on Google any clear explanation. Thanks.