An added complication might arise because the same products, ‘produced’ by the same ‘industries’, can be recorded differently depending on the sector to whom they are sold (e.g. coffee machines sold to corporations will be labeled as capital goods, but when sold to households they’ll be labeled as consumers goods).
If I’m not mistaken, this classification (and aggregation) is dependent on corporations’ reports of capital formation, and not on attributing the corporation’s output to a specific industry.
So even if corporations were ‘pure’ (with regards to industry), it would still be problematic to reconcile industrial imputations and domestic product accounts of recorded capital formation.
Having said that, taking those classifications at face value, and looking at it from the ‘expenditure’ side: is it possible, in principle, to impute shares of income (profits/wages/etc.) to ‘gross investment’/’capital formation’ – based on aggregated data from corporations individual reports? Without recourse to industrial classification.