Ask HN: How to architect modular web applications?

Depends on your language of choice.

I find that an object oriented approach works well for my projects. I write the core class structure for the shared low-level and common high level functionality. I then create a separate directory for each client. In these, I use inheritance to inject custom sub-classes. In extreme cases, I will replace one module with another.

Check out existing open-source projects that have done the same thing. There are bound to be many in whatever language you're using.

you can look at various MVC-based frameworks. they are by default modular.