It's hard to answer the question without more information.   Based on limited knowledge, i would suggest using an account dimension to differentiate the "account".  If you really want to change the account major, i think you could modify the automatic journal to do this.   Not sure how company is defined or anything else though, i'm guessing.

I agree in principle. It is what I also have in mind. 

This means for each combination of dimensions, whether its balance sheet or income statement accounts, a unque general account will exist. 

It means if just one of the 9 dimensions are different, the general ledger account will be different. What I am struggling to wrap my head around, if the same dimension combination are are used for e.g. Sales except the site dimension it will be a different general ledger account. Each of the 20 companies will have a different sales accounts. I am trying to figure out how will these different accounts be dynamically selected in a sales transaction based on the company or site. 

I hope my question make sense

With dimension you only use the dimension on the accounts that you need them on.   So you might just use these on Sales and COGS only. 

>>site dimension it will be a different general ledger account

Are the companies all also financial sites?   

No, not all sites are financial sites, but we made provision for a site dimension to be able to have an income statement even for non financial sites. 

The biggest impact on these are income statement accounts.