My experience is that it is usually better to implement complex arduino code (i.e. easier to write, maintain and share) without modifying the low level interrupt handlers, so I am not the right person to take you down that path.
But if you want, I can try and help you structure your sketch so that your application works as you need without interrupts. If you post your sketch with a brief overview of what functionality you want to have then there may be a simple way to add the capability you need without resorting to modifying arduino hardware interrupt handlers.
There are some applications that modifying the UART interrupt may be a good choice, but it may not be necessary just because there is lots of code doing lots of tasks. My first arduino sketch monitored the serial port while: reading a pot value and switch setting, updating an LCD display, driving a servo, reading the signal from a Radio control transmitter and monitor battery voltage. This was implemented by coding all the services as a separate function which are polled in the main loop. I also wrote my own simple delay function so that the serial port could be constantly monitored even when the sketch was waiting for a long delay.
Let me know if you want to consider doing something like this in your sketch.
Have fun!