I’m going to take a shot at this..??.
Company A makes widgets and pay a 35% corporate tax so company A passes on his cost of goods including his tax liability to Company B that assembles the widgets into a product they retail. Company B may buy gadgets and materiel from multiple vendors, all of which pay 35% tax and include it in the final products they sell. Company B must pass on all their costs including their 35% tax in order to earn a profit.
You forgot that the current 35% tax is on profits, not income. Most companies have a small margin, so they pay 35% on a small amount of their revenue.
Cain eliminates their deductions, so they pay 9% on almost all of their added value. That's why most people who are studying the plan call the business tax a VAT, because it isn't a profits tax.