smc

Doing the addition as is, we get $641+852+973=2466$. This number is $10$ larger than the desired sum of $2456$. Therefore, we must make one of the three numbers $10$ smaller. We may either change $641\to 631$, $852\to 842$, or $973\to 963$. Either change results in a valid sum. The largest digit that could be changed is thus the $7$ in the number $973$, and the answer is $\boxed{7}$.