You have just given basic type and expecting answer on this.
Anyhow as Vikram mentioned above standard works as it is.
So please check if you are using standard message type and call ,then try to find exit and see if you can get the desired error message in there and if yes then you can update error message for yourself.
And if you are hitting custom code for processing then you are the king do whatever your requirement ask.
But again as Vikram pointed out there is no need update multiple message and make it more confusing.
You can decide based on your need.