We have a very old application using .Net Framework 4 that we want to update and start using services instead of one monolithic application.
We ship the same application for every customer, often tho, we have custom code for customers. Up to know we have cloned the project and overriden the specific methods.

We want to create services using .net core web api. So my question is: to still support custom code but make it more managable, is it possible to have a "base" web api project implementing all the endpoints and use that inside another web api project as for example a middleware, so we can implement customer specific stuff inside the project that uses the middleware?
Say the base project implements GET "api/customers/", we want to change the behaviour for this endpoint heavily so we want to custom code only it. So we create the same endpoint on the customer project using the base project as middleware and simply write the custom code inside there so that get's called instead of the endpoint in the base project.

Is it even possible to use another .net core web api porject like that inside another? Does that seem like a good approach or do you have other ideas on how to implement this?