Merging video chunks while streaming (on-the-fly)

The setup:

• Video chunks of 200M
• An nginx server with the mp4 streaming module to serve the video

Is it possible to create a single mp4 file from the chunks, without interruptions to streaming them to the client?

I've tried manually to cat file_chunk >> test.mp4 with a limited success. It works on one occasion (using vlc to play the file while doing cat ...), and doesn't work in different cases (streaming through a browser, using totem media player...).

Additionally, we are using Node.js for authentication and for the API in question (if that may somehow help).

The relevant nginx configuration:

 server {
        listen 441;
        ssl on;
        ssl_certificate /etc/nginx/ssl/server.crt;
                ssl_certificate_key /etc/nginx/ssl/server.key; 
        root /video/;

        location *.mp4 {
            mp4;
            mp4_buffer_size 1m;
            mp4_max_buffer_size 5m;
        }
    }    

Ideally, this could be somewhere in the lines of merging the chunks into a single file which is being streamed (without interruptions).