You should, however, be able to use the same EA with the same magic number for multiple symbols without needing to change anything. Just as long as the orders are selected for processing by their symbol (which they should be).
The only scenario where you would need a different magic number should be if you used the same EA on the same symbol but on different timeframes. Then you would need different magic numbers to ensure that the M5 instance didn't close trades from the M30 instance and vice-versa.