classic asp is a scripting language and does not need to be compiled, so you can override files in production to your heart's content.
MVC however requires compilation, temp files are created and used. As such
you cannot simply override dlls in a running system, the dlls will be in use.
You will need to stop your application which will kill all connections and not accept any more requests, do the upload, recompile your application and then restart it.
All this is usually done very quickly with a CI/CD pipeline. You will probably want to create a process around this, maybe make the website unavailable for a while, but this depends on what kind of system you are running and how critical it is. If you need it up 24/7 without any downtime then you'll need some creative ideas