We ran into this the other day, for the first time.
Swedish/Ottoman foot that has not fired previously receives a bonus +4 dice for melee (first bound).
We assumed that the original battalion involved, which has received the +4, loses the first fire bonus subsequent to the melee.
However, what about reinforcing battalions that have also withheld their first fire? Do they receive the +4, even though they cannot legally fire into melee (the bonus represents very close range shooting as per the rules). Do they NOT receive the +4, but keep their first fire bonus for later shooting?
As umpire, I ruled that the reinforcing foot did not get the +4, but also kept their first fire bonus as they went in with the cold steel.