State Withholding

What have other companies done to setup reciprocal state withholding?

This becomes an issue only when the primary state withholding is higher than the withholding in the state for the construction project.

Connecticut is our primary (HQ) state.

We have projects in MA, NY and RI.

In the long run the employee has to pay the difference when they file taxes.

However, has anyone found a work-around where 2 state withholdings are calculated and if the primary state is higher the 

employee is charged the differential in the primary state.