This should not be a problem at all. ARC Manager also has a built in feature to help users when applying multiple payments to the same invoice on the same day. After applying the first partial payment, when a user goes to apply the second payment, the partially applied invoice amount will be in RED...indicating that something has already been applied. Then, when a user moves the mouse pointer to the RED invoice amount, it will show what has been applied and what balance is remaining. The post back file will contain 2 separate transactions being applied to the open invoice, but that should not be an issue either.
If the payments come on separate days, the first will be an under payment and then the open invoice (in the next days Daily File), will have the balance...and the user can apply the second payment as they would normally do.