Multi-sector analysis

I’m estimating the impacts of large infrastructure project on a state economy. I have a fairly detailed cost budget for construction items, and have allocated the costs to different sectors in the model. All of the money is coming from out of state. Since the construction activity is a true change in final demand (i.e., exogenous to the model) consisting of new money coming into the state, would be there be any double counting among sectors I’ve included if they are linked via inter-industry sales- in other words, if Sector A is included in Sector B’s production function or vice versa. For instance, assume Sector A is a part of Sector B’s production function. If $200 worth of construction funds is going to Sector B and$100 is going to Sector A, these are separate transactions. Wouldn’t the indirect increase in Sector B captured by Sector A’s multiplier be additive rather than duplicative since construction funds are final demand and exogenous to the model? I do understand that problems can arise when using multiple sectors, when we are dealing with a contribution type study (e.g., “What the economic impact of the existing livestock industry to a region?”). In this case, if we estimated the impacts of existing activity with no final demand changes for multiple sectors such as ranches, feedlots, meat processors and so forth, we could not simply sum the impacts across all sectors. This would be double counting because there is no change in final demand. We would have to zero out some RPCs in the production functions for feedlots and ranches since indirect multipliers for meat processors would capture some of this activity. But if it there is a final demand change then I don’t think we would be double counting. Is my logic correct here, or am I missing something obvious?