Isn't this called inheritance? Having classes extend from base classes by adding custom functionality. Whenever I have a large number of If's or cases, I question whether I should refactor into multiple classes.
I would be tempted to arrange things so that customization is in text-form (possibly XML, but I guess that's not the only option), and the main application is generic, and gets the customer specific features by parsing those configuration files.
You could then have a repository for each customer, containing configuration files (and possibly resources, like logos, and/or custom scripts), and a repository for the main application.
For a given customer version, your build system then automatically gathers the application and the customer's repository, and builds the custom version.
I have experience with such a system, and you can get quite extensive customization that way. It makes things a little bit more complex on the application side at first, because you need to add parsing functionality, but it makes management of various customer versions a lot simpler, and somewhat less error prone.
A DI framework in combination with inheritance could keep your system in accord to Open/Closed principle, would make it more modular, and would resolve lifecycle and distribution problem, like when you need to distribute a base library that was extended for a specific customer.
For example, you can have a class Transfer in BaseLibrary and then you can have a class LoggingTransfer extends Transfer in CustomerX library that contains only the code that customizes the base functionality.